Answer:
a) 0.778
b) 0.9222
c) 0.6826
d) 0.3174
e) 2 drivers
Step-by-step explanation:
Given:
Sample size, n = 5
P = 40% = 0.4
a) Probability that none of the drivers shows evidence of intoxication.
[tex] P(x=0) = ^nC_x P^x (1-P)^n^-^x[/tex]
[tex]P(x=0) = ^5C_0 (0.4)^0 (1-0.4)^5^-^0[/tex]
[tex] P(x=0) = ^5C_0 (0.4)^0 (0.60)^5[/tex]
[tex] P(x=0) = 0.778 [/tex]
b) Probability that at least one of the drivers shows evidence of intoxication would be:
P(X ≥ 1) = 1 - P(X < 1)
[tex] = 1 - P(X = 0) [/tex]
[tex] = 1 - ^5C_0 (0.4)^0 * (0.6)^5[/tex]
[tex] = 1 - 0.0778 [/tex]
[tex] = 0.9222 [/tex]
c) The probability that at most two of the drivers show evidence of intoxication.
P(x≤2) = P(X = 0) + P(X = 1) + P(X = 2)
[tex] ^5C_0 (0.4)^0 (0.6)^5 + ^5C_1 (0.4)^1 (0.6)^4 + ^5C_2 (0.4)^2 (0.6)^3 [/tex]
[tex] = 0.6826 [/tex]
d) Probability that more than two of the drivers show evidence of intoxication.
P(x>2) = 1 - P(X ≤ 2)
[tex] = 1 - [^5C_0 (0.4)^0 (0.6)^5 + ^5C_1 (0.4)^1 (0.6)^4 + ^5C_2 * (0.4)^2 (0.6)^3] [/tex]
[tex] = 1 - 0.6826 [/tex]
[tex] = 0.3174 [/tex]
e) Expected number of intoxicated drivers.
To find this, use:
Sample size multiplied by sample proportion
n * p
= 5 * 0.40
= 2
Expected number of intoxicated drivers would be 2
SOMEONE PLEASE HELP ME ASAP PLEASE!!!!
Area of the triangle: 1/2 x 6 x 8 = 24 square ft.
Area of half circle: 1/2 x 3.14 x 4^2 = 25.12 square feet.
Total area : 24 + 25.12 = 49.12 square feet.
A student said that the y-intercept of the function y = 3 · 4x is 4. What is their mistake? What is the actual y-intercept?
Answer:
The y intercept is 0Step-by-step explanation:
the equation of a line is given as
[tex]y= mx+c[/tex]
where
m= is the slope
c= is the y intercept
their mistake is that they did not recall that if the "c" is not shown, it is assumed to be zero (0)
Please show work for number 3 and 4!
Answer:
Three: x = 400
Four : 9
Step-by-step explanation:
Three
a = 10*√2
2a = √(2x) Square both sides.
4a^2 = 2x Divide both sides by 2
2a^2 = x Put a = 10√2 into a^2
2(10√2)^2 = x Square a
2(100*2) = x Multiply the result by 2.
2(200) = x
x = 400
Four
x^(a^2) / x ^(b^2) = x^36
Substitute a + b = 4 in for b.
x^(a^2) / x^(4 - a)^2 = x^36
Subtract powers
x^(a^2 - (4 - a)^2 = x^36
x^(a^2 - (16 - 8a + a^2) = x^36
Gather like terms
x^(8a - 16) = x^36
The powers are now equal
8a - 16 = 36
Add 16 to both sides
8a = 36 + 16
8a = 52
Divide by 8
a = 6.5
Solve for b
a + b = 4
6.5 + b = 4
b = 4 - 6.5
b = - 2.5
a - b = 6.5 - (- 2.5) = 9
Assume the distribution of commute times to a major city follows the normal probability distribution, and the standard deviation is 4.2 minutes. A random sample of 13 commute times is given below in minutes. Find the 98% confidence interval for the mean travel time in minutes. Round your answers to two decimal places and use ascending order.
Answer:
The 98% CI for the mean travel time to the major city is [20.70; 26.14]minutes
Step-by-step explanation:
Hello!
The variable of interest is
X: commute time to a major city.
This variable has a normal distribution
X~N(μ;σ²)
The standard deviation is known to be:
σ= 4.2 minutes
A random sample of n= 13 commute times was taken:
11.5, 13.2, 14.7, 17.1, 18.7, 21.8, 22.4, 25, 26.9, 27.6, 31.1, 35.9, 38.6
You need to estimate the population mean travel time by calculating a 98% CI.
Since the variable has a normal distribution and the population standard deviation is known ,the statistic to use for this interval is the standard normal, then the formula for the interval is:
[X[bar] ± [tex]Z_{1-\alpha /2}[/tex] * [tex]\frac{Sigma}{\sqrt{n} }[/tex]]
The value of the statistic for the 1 - α: 0.98 interval is:
[tex]Z_{1-\alpha /2}= Z_{0.99}= 2.334[/tex]
Next is to calculate the sample mean:
X[bar]= ∑X/n= 304.5/13= 23.42 minutes
[23.42 ± 2.334 * ([tex]\frac{4.2}{\sqrt{13} }[/tex])]
[20.70; 26.14]minutes
With a 98% confidence level you'd expect that the interval [20.70; 26.14]minutes will contain the true mean travel time to the major city.
I hope this helps!
You might need:
A circle is centered at J(3,3) and has a radius of 12.
Where does the point F(-6, -5) lie?
Choose 1 answer:
Answer:
Step-by-step explanation:
The equation of this circle is (x - 3)^2 + (y - 3)^2 = 12^2.
Let's substitute the coordinates of the given point and compare the results to the above equation: do they produce a correct statement?
(-6 - 3)^2 + (-5 - 3)^2 = ?
9^2 + 8^2 = 145
Because r = 12, the above result would need to be 144, not 145, if the given point were actually on the circle. We must conclude that (-6, -5) lies just outside the circle.
81 + 64 = 144
If AYWZ - AYXW, what is true about ZXWZ?
O ZXWZ is an obtuse angle.
ZXWZ is a right angle,
ZXWZ is congruent to ZWXY.
ZXWZ is congruent to ZXZW.
Answer:
<XWZ is a right angle
Step-by-step explanation:
Since <YWZ and <XWY both equal 45 degrees, So, <XWZ is a right angle.
Given that ΔYWZ and ΔYXW are similar triangles, the statement that is true about ΔYXW is: B. XWZ is a right angle,
Similar TrianglesTriangles that are similar possess equal corresponding angles.
We are given that:
ΔYWZ ~ ΔYXW
Therefore:∠YWZ = ∠XWY = 45 degrees
Thus:∠YWZ + ∠XWY = ∠XWZ
45 + 45 = ∠XWZ
∠XWZ = 90 degrees (right angle).
Therefore, given that ΔYWZ and ΔYXW are similar triangles, the statement that is true about ΔYXW is: B. XWZ is a right angle,
Learn more about similar triangles on:
https://brainly.com/question/2644832
The standard form of an absolute value function is f(x) = a|x- h| + k. Which of the following represents the vertex?
(-k,h)
(-h,k)
(k,h)
(h,k)
Answer:
(h, k) is the point that represents the vertex of this absolute value function
Step-by-step explanation:
Recall that the vertex of an absolute value function occurs when the expression within the absolute value symbol becomes "zero", because it is at this point that the results in sign differ for x-values to the left and x-values to the right of this boundary point.
Therefore, in your case, the vertex occurs at x = h, and when x = h, then you can find the y-value of the vertex by looking at what f(h) renders:
f(h) = a | h - h | + k = 0 + k = k
Then the point of the vertex is: (h, k)
Answer:
D on edg2020
Step-by-step explanation:
Took the test
Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $10,100 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,100 and $14,700. Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)
Answer:
[tex] P(X<12000)[/tex]
And for this case we can use the cumulative distribution function given by:
[tex] P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]
And using this formula we have this:
[tex] P(X<12000)= \frac{12000-10100}{14700-10100}= 0.41[/tex]
Then we can conclude that the probability that your bid will be accepted would be 0.41
Step-by-step explanation:
Let X the random variable of interest "the bid offered" and we know that the distribution for this random variable is given by:
[tex] X \sim Unif( a= 10100, b =14700)[/tex]
If your offer is accepted is because your bid is higher than the others. And we want to find the following probability:
[tex] P(X<12000)[/tex]
And for this case we can use the cumulative distribution function given by:
[tex] P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]
And using this formula we have this:
[tex] P(X<12000)= \frac{12000-10100}{14700-10100}= 0.41[/tex]
Then we can conclude that the probability that your bid will be accepted would be 0.41
10-10-10-10-10-10-10
Answer:
-50
Step-by-step explanation:
10-10(5)
Or regular
10-10 = 0
-10 = -10
4 times
-10(4) = 40
-->
-10 - 40 = -50
-50
Answer:
-50
Step-by-step explanation:
5.27 + 3.5
Find the value of
7.9 - 4.36
Give your answer as a decimal.
Write down all the figures on your
calculator display.
Answer:
The value of 7.9-4.36 is 3.54
The value of 5.27 + 3.5 is 8.77
Step-by-step explanation:
A right triangle has sides of lengths 18 , 24 , and 30 units. What is the area of the triangle? Draw the shape on a grid to help find the area.
Answer:216
Step-by-step explanation:The formula to find the area of a triangle is Length times Base divided by 2. The length of the triangle could be 18 or 24, but that doesn’t matter. The base could also be 18 or 24, but that also doesn’t matter, because the hypotenuse (the longest part of a right triangle, in this case being 30), is not a part of the formula. 18 times 24 is 432, and 432 divided by 2 is 216. So the area is 216
please help, me find the area of Letter E.
Answer:
7.005 m^2.
Step-by-step explanation:
We can split this into one vertical rectangle 3.45 * 0.9 m^2
2 rectangles 2 * 0.75 = 1.5 m^2
1 rectangle 1.2 * 0.75 m^2
= 3.105 + 2 * 1.5 + 0.9
= 7.005 m^2.
In similar polygons, corresponding angles should not have equal measures.
True or false
Answer:
The answer is false
Step-by-step explanation:
For two polygons to be similar, both of the following must be true: Corresponding angles are congruent. Corresponding sides are proportional.
PLEASEEEE HELLLPPPP COMPARING EXPONENTIAL FUNCTIONS ...an online retailer developed two exponential functions to model the weekly usage of two coupon codes where x os the number of weeks since the start of the year.
Answer:
A. The weekly usage of both coupons is decreasing and approaching a horizontal asymptote as x gets larger.
Step-by-step explanation:
You can see that f(x) is a decreasing exponential function because the base is 0.75, a value less than 1. The horizontal asymptote is 10, the constant added to the exponential term.
Obviously, g(x) is decreasing. If we assume it is an exponential function, we know there is a horizontal asymptote. (Every exponential function has a horizontal asymptote.)
__
If you use your graphing calculator's exponential regression function, you can find a good model for g(x) is ...
g(x) = 950·0.7^x +12
That is, it is an exponential function that decays faster than f(x), but has a higher horizontal asymptote.
_____
Both functions are decreasing and approaching horizontal asymptotes.
find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (hint: Let (x,y) be the unknown endpoint. Apply the midpoint formula, and solve the two equations for X and y.) midpoint (3,9), endpoint (10,15)
The other endpoint is?
Answer:
(x, y) = (-4, 3)
Step-by-step explanation:
For midpoint M of segment AB, we must have ...
M = (A+B)/2
2M = A+B
B = 2M -A
In terms of x and y, for the given points, we have ...
(x, y) = 2(3, 9) -(10, 15) = (6-10, 18-15)
(x, y) = (-4, 3)
Keisha, a scheduler at Mangel-Wurzel Transport, gets a call from a regular customer needing to move 70.3 m^3 of rock and soil, which Keisha knows from previous experience has an average density of 880 kg/m^3. Keisha has available a dump truck with a capacity of 9 m^3 and a maximum safe load of 5300. kg. Calculate the number of trips the dump truck will have to make to haul the customer's load away.
Answer:
Step-by-step explanation:
You take 70.3m^3 multiple with 880kg /m^3 divide with 5300.kg will give you the answer cause I tried it and it worked 100% true.
I hope tis helps .
A study conducted by Harvard Business School recorded the amount of time CEOs devoted to various activities during the workweek. Meetings were the single largest activity averaging 18 hours per week. Assume that the standard deviation for the time spent in meetings is 5.2 hours. To confirm these results, a random sample of 35 CEOs was selected. This sample averaged 16.8 hours per week in meetings. Which of the following statements is correct?
a. The interval that contains 95% of the sample means is 16.3 and 19.7 hours. Because the sample mean is between these two values, we have support for the results of the CEO study by the Harvard Business School.
b. The interval that contains 95% of the sample means is 17.1 and 18.9 hours. Because the sample mean is not between these two values, we do not have support for the results of the CEO study by the Harvard Business School.
c. The interval that contains 95% of the sample means is 15.7 and 20.3 hours. Because the sample mean is between these two values, we have support for the results of the CEO study by the Harvard Business School.
d. The interval that contains 95% of the sample means is 15.7 and 20.3 hours. Because the sample mean is between these two values, we do not have support for the results of the CEO study by the Harvard Business School
Answer:
a. The interval that contains 95% of the sample means is 16.3 and 19.7 hours. Because the sample mean is between these two values, we have support for the results of the CEO study by the Harvard Business School.
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.
In this question, we have that:
[tex]\mu = 18, \sigma = 5.2, n = 35, s = \frac{5.2}{\sqrt{35}} = 0.879[/tex]
95% of the sample means:
From the: 50 - (95/2) = 2.5th percentile.
To the: 50 + (95/2) = 97.5th percentile.
2.5th percentile:
X when Z has a pvalue of 0.025. So X when Z = -1.96.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-1.96 = \frac{X - 18}{0.879}[/tex]
[tex]X - 18 = -1.96*0.879[/tex]
[tex]X = 16.3[/tex]
97.5th percentile:
X when Z has a pvalue of 0.975. So X when Z = 1.96.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.96 = \frac{X - 18}{0.879}[/tex]
[tex]X - 18 = 1.96*0.879[/tex]
[tex]X = 19.7[/tex]
95% of the sample means are between 16.3 and 19.7 hours. This interval contains the sample mean of 16.8 hours, which supports the study.
So the correct answer is:
a. The interval that contains 95% of the sample means is 16.3 and 19.7 hours. Because the sample mean is between these two values, we have support for the results of the CEO study by the Harvard Business School.
The FDA regulates that fresh Albacore tuna fish that is consumed is allowed to contain 0.82 ppm of mercury or less. A laboratory is estimating the amount of mercury in tuna fish for a new company and needs to have a margin of error within 0.023 ppm of mercury with 97% confidence. Assume the population standard deviation is 0.143 ppm of mercury. What sample size is needed? Round up to the nearest integer, do not include any decimals. Answer:
Answer:
[tex]n=(\frac{2.17(0.143)}{0.023})^2 =182.03 \approx 183[/tex]
So the answer for this case would be n=183 rounded up to the nearest integer
Step-by-step explanation:
Information provided
[tex]\bar X[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma = 0.143[/tex] represent the population standard deviation
n represent the sample size
[tex] ME = 0.023[/tex] the margin of error desired
Solution to the problem
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =0.023 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The confidence level is 97% or 0.97 and the significance would be [tex]\alpha=1-0.97=0.03[/tex] and [tex]\alpha/2 = 0.015[/tex] then the critical value would be: [tex]z_{\alpha/2}=2.17[/tex], replacing into formula (5) we got:
[tex]n=(\frac{2.17(0.143)}{0.023})^2 =182.03 \approx 183[/tex]
So the answer for this case would be n=183 rounded up to the nearest integer
On August 1, 2021, a company accepts an $8,000, 9-month note receivable. For 2021, the company reports interest revenue of $200. What is the interest rate on the note?
Answer:
6%
Step-by-step explanation:
We have to calculate the interest rate in the note, we must follow the following steps, calculate the amount of time remaining from the year 2021, as follows:
interest is for 5 months i.e. from Aug 01 to Dec 31 for year 2021 , so it means it would be 5/12 months.
We have to calculate the interest as follows:
I = P * R * T
We replace:
200 = 8000 * R * 5/12
we solve for R
200 * 12/5 = 8000 * R
R * 8000 = 480
R = 480/8000
R = 0.06
Which means that the interest rate on the note is 6%
justify each step x/3-7=11 x/3=18 x=6
This is the steps for equation solving for the value of x,
x/3-7 = 11
now 7 goes to the other side of equation by changing the sign from - to +,
x/3 = 11 + 7
x/3 = 18
now when we multiply both sides of equation with 3 or 3 goes to the other side of equation and multiply with 18 leaving x alone here for finding the value of x,
and we get, x = 54
at the end of equation we get x = 54, if the equation was in the form 3x - 7 = 11, then we will get x = 6
Expressions equivalent to 7(-3/4x-3)
Answer:-5.25x-21
Step-by-step explanation:7 * -3/4x = -5.25x
7 * -3 = -21
7(-3/4x-3)= -5.25x - 21
5+10/x=x+8 Solve the equation with steps
Answer:
2 and -5
Step-by-step explanation:
[tex]5+\dfrac{10}{x}=x+8 \\\\\\-3+\dfrac{10}{x}=x \\\\\\-3x+10=x^2 \\\\\\x^2+3x-10=0 \\\\\\(x+5)(x-2)=0 \\\\\\x=2,-5[/tex]
Hope this helps!
Which shows how to solve the equation 7x--for x in one step?
X=-6
3
(4)X = -6(4)
(4)X = -6(3)
(9)
3
X=-6
Answer:
the answer is the first option
If sin(18+x)=cos58 find value of x
Answer:
14
Step-by-step explanation:
Since sine and cosine are cofunctions of each other:
[tex]\sin (\theta)= \cos (90-\theta)[/tex]
and vice versa. Therefore:
[tex]18+x=90-58 \\\\18+x=32 \\\\x=32-18=14[/tex]
Hope this helps!
A university with a high water bill is interested in estimating the mean amount of time that students spend in the shower each day. In a sample of 11 students, the average time was 5.33 minutes and the standard deviation was 1.33 minutes. Using this sample information, construct a 99% confidence interval for the mean amount of time that students spend in the shower each day. Assume normality.a) What is the lower limit of the 99% interval? Give your answer to three decimal places.
b) What is the upper limit of the 99% interval? Give your answer to three decimal places.
Answer:
a) lower limit = 4.295 minutes
b) upper limit = 6.365 minutes
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = 5.33 minutes
Standard deviation r = 1.33 minutes
Number of samples n = 11
Confidence interval = 99%
z(at 99% confidence) = 2.58
Substituting the values we have;
5.33+/-2.58(1.33/√11)
5.33+/-2.58(0.401010088288)
5.33+/-1.0346060277
5.33+/-1.035
= ( 4.295, 6.365) minutes
Therefore at 99% confidence interval (lower, upper limit) = ( 4.295, 6.365) minutes
a) lower limit = 4.295 minutes
b) upper limit = 6.365 minutes
Company A is trying to sell its website to Company B. As part of the sale, Company A claims that the average user of their site stays on the site for 10 minutes. Company B is concerned that the mean time is significantly less than 10 minutes. Company B collects the times (in minutes) below for a sample of 19 users. Assume normality.
Time: 1.2, 2.8, 1.5, 19.3, 2.4, 0.7, 2.2, 0.7, 18.8, 6.1, 6, 1.7, 29.1, 2.6, 0.2, 10.2, 5.1, 0.9, 8.2
Conduct the appropriate hypothesis test for Company B using a 0.08 level of significance.
a) What is the critical value for the test? Give your answer to four decimals.
b) What is the appropriate conclusion?
A. Reject the claim that the mean time is 10 minutes because the test statistic is larger than the critical point.
B. Fail to reject the claim that the mean time is 10 minutes because the test statistic is larger than the critical point.
C. Reject the claim that the mean time is 10 minutes because the test statistic is smaller than the critical point.
D. Fail to reject the claim that the mean time is 10 minutes because the test statistic is smaller than the critical point.
Answer:
a) Critical value = -1.4052
Since we are checking if the mean time is less than 10 minutes, the rejection area would be
z < -1.4052
b) Option C is correct.
Reject the claim that the mean time is 10 minutes because the test statistic is smaller than the critical point.
That is, the mean time is significantly less than 10 minutes.
Step-by-Step Explanation:
a) Using z-distribution, the critical value is obtained from the confidence level at which the test is going to be performed. Since the hypothesis test tests only in one direction (checking if the claim is less than 10 minutes significantly)
P(z < Critical value) = 0.08
From the z-tables, critical value = -1.4052
Since we are checking if the mean time is less than 10 minutes, the rejection area would be
z < -1.4052
b) We first give the null and alternative hypothesis
The null hypothesis is that there isn't significant evidence to suggest that the mean time is less than 10 minutes.
And the alternative hypothesis is is that there is significant evidence to suggest that the mean time is less than 10 minutes.
To now perform this hypothesis test, we need to obtain the test statistic
Test statistic = (x - μ)/σₓ
x = sample mean = (Σx/N)
The data is
1.2, 2.8, 1.5, 19.3, 2.4, 0.7, 2.2, 0.7, 18.8, 6.1, 6, 1.7, 29.1, 2.6, 0.2, 10.2, 5.1, 0.9, 8.2
Σx = 119.7
N = Sample size = 19
x = sample mean = (119.7/19) = 6.3
μ = standard to be compared against = 10 minutes
σₓ = standard error = (σ/√N)
where N = Sample size = 19
σ = √[Σ(x - xbar)²/N]
x = each variable
xbar = mean = 6.3
N = Sample size = 19
Σ(x - xbar)² = 1122.74
σ = (√1122.74/19) = 7.687
σₓ = (7.687/√19) = 1.7635
Test statistic = (x - μ)/σₓ
Test statistic = (6.3 - 10)/1.7635
= -2.098 = -2.10
z = -2.10 and is in the rejection region, (z < -1.4052), hence, we reject the null hypothesis and the claim and say that the mean time is significantly less than 10 minutes.
The test statistic is less than the critical point, hence, we reject the null hypothesis and the claim and conclude that the mean time is less than 10 minutes.
Hope this Helps!!!
The critical value for the test based on the sampling distribution is -1.4052 and one needs to reject the claim.
How to explain the sampling distribution?From the complete information given, the descriptive statistics from the sample information has been given. The sample mean and variance are given. Therefore, the value of the test statistics from the information is -1.4052.
Also, the conclusion is to reject the claim since the test statistic is smaller than the critical point.
Therefore, the correct option is to reject the claim that the mean time is 10 minutes because the test statistic is smaller than the critical point.
Learn more about sampling on:
https://brainly.com/question/17831271
if segment ac and segment bc are tangent to circle o find the value of x
Answer:
x = 150°
Step-by-step explanation:
Start by cutting the shape into two triangles by bisecting the 30°
Now we have two triangles that have two angles 90° and 15°
Subtract 15° from 90°, you'll get 75°
Double 75° because x is split into 2
150° = x
Also, were given 3 angles, this is a quadrilateral.
90° + 90° + 30° = 210°
360° - 210° = 150°
Answer:
150°
Step-by-step explanation:
OA⊥AC and OB⊥BC
∠A+∠B+∠C+∠O=360°
90°×2+30°+x=360°
x=360°-210°=150°
Nick,Sarah and Gavyn share some sweets on the ratio 6:2:1. Nick gets 30 more sweets than Gavyn. How many sweets does Sarah get?
Answer:
12
Step-by-step explanation:
N:S:G
6:2:1
Nick gets 30 more sweets than Gavyn, therefore we can say that.
[tex]6x=x+30\\5x=30\\x=6[/tex]
As Sarah gets twice the amount of sweets that Gavyn does.
[tex]2(6)=12[/tex]
Find the vertex of the graphed function.
f(x) = |x-4| +3
AY
00
6
4
2
Y
4
The vertex is at
Answer:
The x-coordinate is the solution to x - 4 = 0, which is x = 4 and the y-coordinate is 3 so the answer is (4, 3).
The demand for the video games provided by Mid-Tech Video Games Inc. has exploded in the last several years. Hence, the owner needs to hire several new technical people to keep up with the demand. Mid-Tech gives each applicant a special test that Dr. McGraw, the designer of the test, believes is closely related to the ability to create video games. For the general population, the mean on this test is 100. Below are the scores on this first test for the applicants. 95 105 120 81 90 115 99 100 130 10 The owner is interested in the overall quality of the job applicants based on this test. Compute the mean and the median scores for the 10 applicants. What would you report to the owner
Answer:
Mean: 94.5.
Median: 99.5
Standard deviation: 33.1
We can tell the owner that the applicants don't have a score significantly below from 100.
Step-by-step explanation:
First, we analize the sample and calculate the statistics (mean, median and standard deviation).
Mean of the sample:
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{10}(95+105+120+81+90+115+99+100+130+10)\\\\\\M=\dfrac{945}{10}\\\\\\M=94.5\\\\\\[/tex]
The median, as the sample size is an even number, can be calculated as the average between the fifth and sixth value, sort by value:
[tex]\text{Median}=\dfrac{99+100}{2}=99.5[/tex]
The standard deviation is:
[tex]s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{9}((95-94.5)^2+(105-94.5)^2+(120-94.5)^2+. . . +(10-94.5)^2)}\\\\\\s=\sqrt{\dfrac{9834.5}{9}}\\\\\\s=\sqrt{1092.7}=33.1\\\\\\[/tex]
To tell if this sample has a value significantly lower than the expected score of 100, we should make a hypothesis test.
The claim is that the mean score is significantly lower than 100.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=100\\\\H_a:\mu< 100[/tex]
The significance level is 0.05.
The sample has a size n=10.
The sample mean is M=94.5.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=33.1.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{33.1}{\sqrt{10}}=10.467[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{94.5-100}{10.467}=\dfrac{-5.5}{10.467}=-0.53[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=10-1=9[/tex]
This test is a left-tailed test, with 9 degrees of freedom and t=-0.53, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-0.53)=0.306[/tex]
As the P-value (0.306) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the mean score is significantly lower than 100.