Answer:
14.69% probability that this happens
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
1000 people were given assurance of a room.
This means that [tex]n = 1000[/tex]
Let us assume that each customer cancels their reservation with a probability of 0.1.
So 0.9 probability that they still keep their booking, which means that [tex]p = 0.9[/tex]
Probability more than 900 still keeps their booking:
[tex]n = 1000, p = 0.9[/tex]
So
[tex]\mu = 0.9, s = \sqrt{\frac{0.9*0.1}{1000}} = 0.0095[/tex]
901/1000 = 0.91
So this is 1 subtracted by the pvalue of Z when X = 0.91.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{0.91 - 0.9}{0.0095}[/tex]
[tex]Z = 1.05[/tex]
[tex]Z = 1.05[/tex] has a pvalue of 0.8531
1 - 0.8531 = 0.1469
14.69% probability that this happens
Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps. This system of equations models the given information for both stamp types. x – y = 34 x + y = 212 Solve the system of equations. How many foreign stamps does Malik have? foreign stamps How many domestic stamps does Malik have? domestic stamps
Answer:
foreign: 89domestic: 123Step-by-step explanation:
Add the two equations together:
(x -y) +(x +y) = (34) +(212)
2x = 246
x = 123
y = x-34 = 89
Malik has 89 foreign stamps and 123 domestic stamps.
Answer:
89 and 123
Step-by-step explanation:
I need help for a grade
Answer:
180
Step-by-step explanation:
2(24)-3=45
24-8=√16=4
45*4=180
A bucket that weighs 4 lb and a rope of negligible weight are used to draw water from a well that is 60 ft deep. The bucket is filled with 42 lb of water and is pulled up at a rate of 1.5 ft/s, but water leaks out of a hole in the bucket at a rate of 0.15 lb/s. Find the work done in pulling the bucket to the top of the well. Show how to approximate the required work by a Riemann sum. (Let x be the height in feet above the bottom of the well. Enter xi* as xi.)
Answer:
2580 ft-lb
Step-by-step explanation:
Water leaks out of the bucket at a rate of [tex]\frac{0.15 \mathrm{lb} / \mathrm{s}}{1.5 \mathrm{ft} / \mathrm{s}}=0.1 \mathrm{lb} / \mathrm{ft}[/tex]
Work done required to pull the bucket to the top of the well is given by integral
[tex]W=\int_{a}^{b} F(x) dx[/tex]
Here, function [tex]F(x)[/tex] is the total weight of the bucket and water [tex]x[/tex] feet above the bottom of the well. That is,
[tex]F(x)=4+(42-0.1 x)[/tex]
[tex]=46-0.1x[/tex]
[tex]a[/tex] is the initial height and [tex]b[/tex] is the maximum height of well. That is,
[tex]a=0 \text { and } b=60[/tex]
Find the work done as,
[tex]W=\int_{a}^{b} F(x) d x[/tex]
[tex]=\int_{0}^{60}(46-0.1 x) dx[/tex]
[tex]&\left.=46x-0.05 x^{2}\right]_{0}^{60}[/tex]
[tex]=(2760-180)-0[[/tex]
[tex]=2580 \mathrm{ft}-\mathrm{lb} [/tex]
Hence, the work done required to pull the bucket to the top of the well is [tex]2580 \mathrm{ft}- \mathrm{lb}[/tex]
How do you determine the vertex from the vertex from of a quadratic equation
Answer:
it it the highest or lowest point of a parabola
Moises read a book that is more than 200 pages long. It took him 10 days, and he read the same number of pages each day. The inequality 10 p greater-than 200 represents the possible values of p, the number of pages he read each day.
Which is a possible value of p?.
10
15
20
25
Answer:
25
Step-by-step explanation:
10p > 200
10 * 10 < 200
10 * 15 < 200
10 * 20 = 200
10 * 25 > 200
Answer:
The answer is D
Step-by-step explanation:
In a lottery daily game, a player picks three numbers from 0 to 9 (without repetition). How many different choices does the player have if order does not matter
Answer:
Not sure 3/10?
Step-by-step explanation:
numbers are 0-9...that's 10 choices.
he chooses 3 numbers
I would think 3/10?
According to statistician Persi Diaconis, the probability of a penny landing heads when it is spun on its edge is only about 0.20. Suppose you doubt this claim and think that it should be more than 0.20. To test this, you spin a penny 12 times and it lands heads side up 5 times. You put this information in the One Proportion applet and determine a simulation-based p-value of 0.0770, but the one-proportion z-test p-value is 0.0303.
Required:
a. Which P-value is the most valid and why?
b. Do you have strong evidence that a spun penny will land heads more that 20% or the time in the long run?
Answer:
a) The p-value obtained from the one-proportion applet is more valid because a z-test statistic shouldn't have been used for the other obtained p-value. Check Explanation for more Explanation.
b) No, there isn't enough evidence to suggest that a spun penny will land heads more that 20% of the time in the long run.
Step-by-step explanation:
The p-value for this problem was obtained from a one proportion simulation applet and another obtained using a one proportion z-test p-value.
But one of the conditions for the use of the z-test or the z-distribution in obtaining the p-value is that information on the population mean and standard deviation should be known or the sample size should be large enough such that the properties of the sample should approximate the properties of the the population distribution.
But for this question and hypothesis test, the sample that the we are working with is only of sample size 12 with no information on the population standard deviation provided, hence, the p-value obtained from the z-test statistic one proportion test is not a valid enough one due to this reason.
Plus, on calculating this p-value manually, it was obtained to be 0.078, to justify this explanation as it is very close to.the value obtained using the simulation applet.
Manual way of calculating
t = (x - μ)/σₓ
x = 5/12 = 0.41667
μ = p₀ = 0.20
σₓ = standard error = √[p(1-p)/n]
where n = Sample size = 12
σₓ = √[0.4167×0.5833/12] = 0.1423
t = (0.4167 - 0.20) ÷ 0.1423
t = 1.52
checking the tables for the p-value of this t-statistic
Degree of freedom = df = n - 1 = 12 - 1 = 11
Significance level = 0.05 (This is used when no significance level is provided in the question)
The hypothesis test uses a one-tailed condition because we're testing only in one direction.
p-value (for t = 1.52, at 0.05 significance level, df = 11, with a one tailed condition) = 0.07836
b) To know which conclusion to draw, we need to first define the null and alternative hypothesis.
The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.
For this question, the null hypothesis is that there isn't enough evidence to suggest that a spun penny will land heads more that 20% of the time in the long run.
And the alternative hypothesis is that there is enough evidence to suggest that a spun penny will land heads more that 20% of the time in the long run.
Mathematically, if p is the proportion of times the spun penny will turn up heads in the long run,
The null hypothesis is represented as
H₀: p ≤ 0.20
The alternative hypothesis is represented as
Hₐ: p > 0.20
The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 0.05 (usually used when the significance level for the test isn't specified)
p-value = 0.0770
0.0770 > 0.05
Hence,
p-value > significance level
This means that we fail to reject the null hypothesis & say there isn't enough evidence to suggest that a spun penny will land heads more that 20% of the time in the long run.
Hope this Helps!!!
A marketing consulting group wants to see whether placing a seasonal cookie product on an end cap (the shelf at the end of an aisle at a store) will make a difference in sales. The average sales of the seasonal cookie for this region was 650 units. A sample of 36 stores that placed the cookie on an end cap showed a sample mean of 671 units sold with a standard deviation of 81. The resulting p-value is 0.1288; thus, the null hypothesis is not rejected. The marketing consulting group concludes that placing the cookies on an end cap does not affect sales. What type of error is possible in this situation
Answer:
Type II error.
Step-by-step explanation:
We have a hypothesis test for the claim that placing a seasonal cookie product on an end cap (the shelf at the end of an aisle at a store) will make a difference in sales.
The null hypothesis will state that there is no difference, while the alternative hypothesis will state that there is significant positive difference.
The result is a P-value of 0.1288 and the null hypothesis failing to be rejected.
As the null hypothesis failed to be rejected, if an error has been made in the conclusion, is that we erroneusly accept a false null hypothesis.
This is a Type II error, where the null hypothesis is accepted although the alternative hypothesis is true.
Find the slope of the line that goes through the given points.
(6,1) and (9,-1)
Answer:
m = -2/3
Step-by-step explanation:
Slope Formula: [tex]m = \frac{y2-y1}{x2-x1}[/tex]
So,
[tex]m = \frac{-1-1}{9-6}[/tex]
m = -2/3
What is the value of AC?
Answer:
0.637
Step-by-step explanation:
The average value of a whole sinusoidal waveform over one complete cycle is zero as the two halves cancel each other out
The distribution of the amount of money spent by students for textbooks in a semester is approximately normal in shape with a mean of $235 and a standard deviation of $20. According to the Standard Deviation Rule, almost all (99.7%) of the students spent on textbooks in a semester:______.A. Between 230 and 240 dollars.B. Between 220 and 250 dollars.C. Between 175 and 295 dollars.D. Less than 220 dollars or more than 250 dollars.E. Less than 230 dollars or more than 240 dollars.
Answer:
C. Between 175 and 295 dollars.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 235
Standard deviation = 20
According to the Standard Deviation Rule, almost all (99.7%) of the students spent on textbooks in a semester:
Within 3 standard deviations of the mean.
235 - 3*20 = 175
235 + 3*20 = 295
So the correct answer is C.
A researcher receives 106 containers of oxygen. Of those containers, twenty of them have oxygen that is not ionized and the rest are ionized. Two samples are randomly selected, without replacement, from the lot. i) What is the probability that the second one selected is not ionized given that the first one was ionized
Answer:
0.1905 = 19.05%
Step-by-step explanation:
We have a total of 106 containers of oxygen, from which:
20 have oxygen not ionized, 86 have oxygen ionized.
If the first one selected is ionized, now we have 20 not ionized and 85 ionized.
So the probability of the second one selected being not ionized is the number of not ionized (20) over the total number of containers (20 + 85):
P = 20 / (20 + 85) = 0.1905 = 19.05%
Two similar circles are shown. The circumference of the larger circle, with radius OB, is 3 times the circumference of the smaller circle, with radius OA. Two circles are shown. The smaller circle has radius O A and the larger circle has radius O B. Radius OB measures x units. Which expression represents the circumference of the smaller circle with radius OA? (StartFraction pi Over 3 EndFraction)x units (StartFraction 2 pi Over 3 EndFraction)x units 2πx units 6πx units
Answer:
its 2pi/3
Step-by-step explanation:
because the full radian measure of a circle is 2pi radians, the smaller circle is a third of the size of the larger one. Multiply straight across for (2pi/1)(1/3)
The circumference of the smaller circle can be given by [tex]\dfrac{2\times \pi}{m}(x)\ units[/tex].
Given to us,Two similar circles are shown.The circumference of the larger circle, with radius OB, is 3 times the circumference of the smaller circle, with radius OA. The smaller circle has radius O A and the larger circle has radius O B. Radius OB measures x units. Circumference of the larger circle[tex]\rm{Circumference\ of\ the\ circle = 2\times \pi \times (radius)[/tex]
[tex]\rm{Circumference\ of\ the\ circle = 2\times \pi \times (OB)[/tex]
[tex]\rm{Circumference\ of\ the\ circle = 2\times \pi \times (x)[/tex]
Circumference of the smaller circle,Circumference of the Larger circle = 3 x Circumference of the smaller circle
[tex]2\times \pi \times x = 3\times Circumference\ of\ the\ smaller\ circle\\\\3\times Circumference\ of\ the\ smaller\ circle = 2\times \pi \times x \\\\Circumference\ of\ the\ smaller\ circle = \dfrac{2\times \pi \times x }{3}\\\\Circumference\ of\ the\ smaller\ circle = \dfrac{2\times \pi}{3}( x )\ units[/tex]
Hence, the circumference of the smaller circle can be given by [tex]\dfrac{2\times \pi}{m}(x)\ units[/tex].
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There is a bag filled with 5 blue and 4 red marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced. Another marble is taken at random. What is the probability of getting exactly 1 blue?
Answer:
5 out of 9
Step-by-step explanation:
You have 5 blue marbles and for red marbles which makes a total of 9 marbles in a bag. If you take one marble out and put it back in another marble out and put it back at random the probability of getting a blue marble is 5 out of 9.
The probability of getting exactly 1 blue marble from a bag which is filled with 5 blue and 4 red marbles is 40/81.
What is probability?Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
There is a bag filled with 5 blue and 4 red marbles. Thus, the total number of marble in the bag are,
[tex]5+4=9[/tex]
One marble is taken at random from the bag, the color is noted and then it is replaced. The probability of getting blue marble is,
[tex]P(B)=\dfrac{5}{9}[/tex]
The probability of getting red marble is,
[tex]P(R)=\dfrac{4}{9}[/tex]
The Probability of getting red marble in first pick and probability of getting blue marble in second pick is,
[tex]P_1=\dfrac{4}{9}\times\dfrac{5}{9}=\dfrac{20}{81}[/tex]
The Probability of getting blue marble in first pick and probability of getting red marble in second pick is,
[tex]P_2=\dfrac{5}{9}\times\dfrac{4}{9}=\dfrac{20}{81}[/tex]
The exactly 1 blue is taken out, when first marble is red and second is blue or the first one is blue and second one is red. Thus, the probability of getting exactly 1 blue is,
[tex]P=P_1+P_2\\P=\dfrac{20}{81}+\dfrac{20}{81}\\P=\dfrac{40}{81}[/tex]
Thus, the probability of getting exactly 1 blue marble from a bag which is filled with 5 blue and 4 red marbles is 40/81.
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What is the ratio 28 : 4 in it's simplest form?
Answer:
7:1
Step-by-step explanation:
28:4=
7(4):1(4)=
7:1
Hope this helps!
Answer:
[tex]7:1[/tex]
Step-by-step explanation:
[tex]28:4[/tex]
Common highest factor is 4.
Simplify the ratio.
[tex]28 \div 4 : 4 \div 4[/tex]
[tex]7:1[/tex]
A contractor is in charge of hiring people for a construction project. The number of days it would take to complete the project with xx full time workers can be found using the function f(x)=\frac{280}{x}.f(x)= x 280 . Assume once workers are assigned to the project, no workers may be added or taken off the project until it is finished. Find and interpret the given function values and determine an appropriate domain for the function.
Answer:
[tex]\text{Domain of x}=[1,\infty), x \in Z^+[/tex]
Step-by-step explanation:
Given the function: [tex]f(x)=\dfrac{280}{x},$ where:[/tex]
f(x) =number of days it would take to complete the project
x =number of full-time workers.
[tex]\text{When x=0, }f(x)=\dfrac{280}{0}=$Undetermined\\\text{When x=1, }f(x)=\dfrac{280}{1}=$280 days\\\text{When x=280, }f(x)=\dfrac{280}{280}=$1 day\\\text{When x=560, }f(x)=\dfrac{280}{560}=$0.5 days[/tex]
The domain of a function is the complete set of possible values of the independent variable.
In this case, the independent variable is x, the number of full-time workers. We have shown that x cannot be zero as there must be at least a worker on ground.
Therefore, an appropriate domain of the function f(x) is the set of positive integers (from 1 to infinity).
[tex]\text{Domain of x}=[1,\infty), x \in Z^+[/tex]
Vitamin D is important for the metabolism of calcium and exposure to sunshine is an important source of vitamin D. A researcher wanted to determine whether osteoperosis was associated with a lack of exposure to sunshine. He selected a sample of 250 women with osteoperosis and an equal number of women without osteoperosis. The two groups were matched - in other words they were similar in terms of age, diet, occupation, and exercise levels. Histories on exposure to sunshine over the previous twenty years were obtained for all women. The total number of hours that each woman had been exposed to sunshine in the previous twenty years was estimated. The amount of exposure to sunshine was compared for the two groups. Group of answer choices
Answer:
The type of observational study describer here is retrospective study.
Step-by-step explanation:
The complete question is:
Vitamin D is important for the metabolism of calcium and exposure to sunshine is an important source of vitamin D. A researcher wanted to determine whether osteoperosis was associated with a lack of exposure to sunshine. He selected a sample of 250 women with osteoperosis and an equal number of women without osteoperosis. The two groups were matched - in other words they were similar in terms of age, diet, occupation, and exercise levels. Histories on exposure to sunshine over the previous twenty years were obtained for all women. The total number of hours that each woman had been exposed to sunshine in the previous twenty years was estimated. The amount of exposure to sunshine was compared for the two groups. Determine what type of observational study is described. Explain.
Solution:
In retrospective study design, the concerned outcome has previously taken place in each participant by the phase he or she is signed up for the study, and the information are gathered either from past data or by requesting the participants to recall exposures.
It is also known as a historic cohort study.
A retrospective study is completed as posterior experiment, using data on events that have already taken place in the history. In most cases some or most of the data has already been collected and stowed in the archive.
In the provided scenario, the researcher collect the past data for the exposure to sunshine over the previous twenty years for 250 women. And estimated the total number of hours that each woman had been exposed to sunshine in the previous twenty years.
Then the researcher compares the amount of exposure to sunshine for the two groups.
Thus, the type of observational study describer here is retrospective study.
According to statcounter, Google Chrome browser controls 62.8% of the market share worldwide. A random sample of 70 users was selected. What is the probability that 35 or more from this sample used Google Chrome as their browser
Answer:
The probability that 35 or more from this sample used Google Chrome as their browser is 0.9838.
Step-by-step explanation:
We are given that according to Statcounter, the Google Chrome browser controls 62.8% of the market share worldwide.
A random sample of 70 users was selected.
Let [tex]\hat p[/tex] = sample proportion of users who used Google Chrome as their browser.
The z-score probability distribution for the sample proportion is given by;
Z = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion = [tex]\frac{35}{70}[/tex] = 0.50
p = population proportion = 62.8%
n = sample of users = 70
Now, the probability that 35 or more from this sample used Google Chrome as their browser is given by = P( [tex]\hat p[/tex] [tex]\geq[/tex] 0.50)
P( [tex]\hat p[/tex] [tex]\geq[/tex] 0.50) = P( [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] [tex]\geq[/tex] [tex]\frac{0.50-0.628}{\sqrt{\frac{0.50(1-0.50)}{70} } }[/tex] ) = P(Z [tex]\geq[/tex] -2.14)
= P(Z [tex]\leq[/tex] 2.14) = 0.9838
The above probability is calculated by looking at the value of x = 2.14 in the z table which has an area of 0.9838.
Graph: Y – 3=1/2(x +2)
Answer:
Step-by-step explanation:y–3=½(x+2)
Multiply through by the denominator (2).
2×y–2×3=½(x+2)×2
2y–6=1(x+2) because the denominator (2) will cancel the other 2 multiplying it
2y–6=x+2
2y=x+2+6
2y=x+8
---. -----
2. 2
•°•y=x+8
-----. Or y=x+4
2
Find the point P on the line yequals=33x that is closest to the point (60 comma 0 )(60,0). What is the least distance between P and (60 comma 0 )(60,0)?
Answer:
[tex]18\sqrt{10}$ units[/tex]
Step-by-step explanation:
We are given the equation of the line y=3x and a point, say Q(60,0) outside of that line.
We want to find the point on the line y=3x which is closest to Q.
Let P(x,y) be the desired point. Since it is on the line y=3x, it must satisfy the line.
If x=a, y=3a, so the point P has the coordinates (a,3a).
Distance between point Q and P
[tex]=\sqrt{(60-a)^2+(0-3a)^2}\\D =\sqrt{10a^2-120a+3600}[/tex]
To minimize D, we find its derivative
[tex]\dfrac{dD}{da}=\dfrac{10a-60}{\sqrt{10a^2-120a+3600} }\\$Setting \dfrac{dD}{da}=0\\10a-60=0\\10a=60\\a=6[/tex]
Therefore, the y-coordinate for P is 3*6=18.
The point P=(6,18).
Next, we calculate the distance between P(6,18) and (60,0).
[tex]D =\sqrt{10(6)^2-120(6)+3600}\\=\sqrt{3240}\\=18\sqrt{10}$ units[/tex]
Approximately 8% of all people have blue eyes. Out of a random sample of 20 people, what is the probability that 2 of them have blue eyes? Round answer to 4 decimal places. Answer:
Answer:
27.11% probability that 2 of them have blue eyes
Step-by-step explanation:
For each person, there are only two possible otucomes. Either they have blue eyes, or they do not. The probability of a person having blue eyes is independent of any other person. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
8% of all people have blue eyes.
This means that [tex]p = 0.08[/tex]
Random sample of 20 people:
This means that [tex]n = 20[/tex]
What is the probability that 2 of them have blue eyes?
This is P(X = 2).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{20,2}.(0.08)^{2}.(0.92)^{18} = 0.2711[/tex]
27.11% probability that 2 of them have blue eyes
The probability that 2 of them have blue eyes is 27.11%.
Given that,
Approximately 8% of all people have blue eyes.
Out of a random sample of 20 people,
We have to determine,
What is the probability that 2 of them have blue eyes?
According to the question,
People having blue eyes p = 8% = 0.08
Sample of people n = 20
For each person, there are only two possible outcomes. Either they have blue eyes, or they do not.
The probability of a person having blue eyes is independent of any other person.
The probability that 2 of them have blue eyes is determined by using a binomial probability distribution.
[tex]\rm P (X = x) =n_C_x\times p^x \times (1-p)^{n-x}}[/tex]
Therefore,
The probability that 2 of them have blue eyes is,
[tex]\rm P (X = x) =n_C_x\times p^x \times (1-p)^{n-x}}\\\\ \rm P (X = x) = \dfrac{n!}{(n-x)! \times x!} \times p^x \times (1-p)^{n-x}}\\\\[/tex]
Substitute all the values in the formula,
[tex]\rm P (X = 2) = \dfrac{20!}{(20-2)! \times 2!} \times (0.08)^2 \times (1-0.08)^{20-2}}\\\\ P (X = 2) = \dfrac{20!}{(18)! \times 2!} \times (0.0064) \times (0.92)^{18}}\\\\ P (X = 2) = \dfrac{19\times 20}{ 2} \times (0.0064) \times (0.222)\\\\ P(X = 2) = {19\times 10}\times (0.00142)\\\\P(X = 2) = 0.2711\\\\P(X = 2) = 27.11 \ Percent[/tex]
Hence, The required probability that 2 of them have blue eyes is 27.11%.
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In 2003, a school population was 903. By 2007 the population had grown to 1311. How much did the population grow between the year 2003 and 2007? How long did it take the population to grow feom 903 students to 1311 students? What is the average population growth per year?
Answer:
The average population growth per year is 102.
Step-by-step explanation:
From the given data, we can find the slope which will give us the average rate of change. Our points are:
[tex](2003, 903)\quad and \quad (2007, 1311)[/tex]
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}=\frac{1311-903}{2007-2003}\\\\m=102[/tex]
Best Regards!
The measure of angle O is 600°. The polnt (x, y) corresponding to on the unit circle is?
Answer:
[tex](\frac{-1}{2} , \frac{-\sqrt{3} }{2} )[/tex]
Step-by-step explanation:
Memorize your unit circle.
Step 1: Subtract 360 from 600 degrees to find rotation
600° - 360° = 240°
Step 2: Either find coordinates from unit circle or convert to radians
240° = 4π/3
Step 3: Find coordinates
The burning times of scented candles, in minutes, are normally distributed with a mean of 249 and a standard deviation of 20. Find the number of minutes a scented candle burns if it burns for a shorter time than 60% of all scented candles.
Answer:
The candle burns for 244 minutes.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 249, \sigma = 20[/tex]
Find the number of minutes a scented candle burns if it burns for a shorter time than 60% of all scented candles.
This is the 100-60 = 40th percentile, which is X when Z has a pvalue of 0.4. So X when Z = -0.253.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.253 = \frac{X - 249}{20}[/tex]
[tex]X - 249 = -0.253*20[/tex]
[tex]X = 244[/tex]
The candle burns for 244 minutes.
insert a digit to make numbers that are divisible by 24 if it is possible 38_36
Answer:
ge
Step-by-step explanation:
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The local food pantry has 1, 600 cans of fruit. They give away 155 cans of fruit each week. Assuming no new donations are made,
how many cans of fruit will remain after 6 weeks?
The solution is
What is the answer for this problem?
Answer:
670 Cans of fruit will be left
Step-by-step explanation:
First you multiply 155 by the 6 weeks.
That equals 930 and then you subtract 930 from 1,600 and that gives you 670.
There are 670 cans of fruit that will remain after 6 weeks the answer is 670 cans.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
We have:
The local food pantry has 1, 600 cans of fruit. They give away 155 cans of fruit each week.
First term a = 1600
Common difference d = -155
After 6 weeks means on week 7.
n = 7
a(7) = 1600 + (7-1)(-155)
a(7) = 1600 - 930
a(7) = 670
Thus, there are 670 cans of fruit that will remain after 6 weeks the answer is 670 cans.
Learn more about the sequence here:
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Find the range of the function f(x) = -x 2 + 4x if the domain is {-2, 0, 1}.
Answer:
y≤4
Step-by-step explanation:
y≤4
try to graph it on a parabola and u will find the answer above :D hope this helped
Solve the equation x^3 + 2x^2 - 11x -12 = 0
Answer: there are 4 solutions
x = -2
x = -1/2 = -0.500
x =(3-√5)/2= 0.382
x =(3+√5)/2= 2.618
Step-by-step explanation:
what are the steps (2+2i)(5+3i)??? please help me
Consider the graph of the line of best fit, y = 0.5x + 1, and the given data points. A graph shows the horizontal axis numbered negative 4 to positive 4 and the vertical axis numbered negative 4 to positive 4. Points show an upward trend. Which is the residual value when x = 2? –2 –1 1 2
Answer
its -1
Step-by-step explanation:
ED 2020 boiiiii
The residual value of the line of the best fit when x = 2 is -1
How to determine the residual value?The equation of the line is given as:
y = 0.5x + 1
When x = 2, we have:
y = 0.5 * 2 + 1
Evaluate
y = 2
The residual is the difference between the actual value and the predicted value.
From the complete graph, the actual value is 1.
So, we have:
Residual = 1 - 2
Evaluate
Residual = -1
Hence, the residual value when x = 2 is -1
Read more about residuals at:
https://brainly.com/question/1168961
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