Answer:
0.0154 = 1.54% probability that average sleeping time for a randomly selected sample of 42 students is more than 6.5 hours per night.
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 = 6.3, \sigma = 0.6, n = 42, s = \frac{0.6}{\sqrt{42}} = 0.0926[/tex]
Find the probability that average sleeping time for a randomly selected sample of 42 students is more than 6.5 hours per night.
This is 1 subtracted by the pvalue of Z when X = 6.5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{6.5 - 6.3}{0.0926}[/tex]
[tex]Z = 2.16[/tex]
[tex]Z = 2.16[/tex] has a pvalue of 0.9846
1 - 0.9846 = 0.0154
So
0.0154 = 1.54% probability that average sleeping time for a randomly selected sample of 42 students is more than 6.5 hours per night.
I'm lost with this problem please help. Write answers as a fractions
Answer: 8/3 and -9/4
Step-by-step explanation:
1. [tex]\frac{2^{3}}{3} = \frac{2 * 2 * 2}{3} = \frac{8}{3}[/tex]
2. In this problem, when raising a whole fraction to a power, you must both raise the numerator and denominator to that power.
[tex]-(\frac{3}{2})^2 = -(\frac{3^2}{2^2}) = -(\frac{9}{4}) = -\frac{9}{4}[/tex]
Halfway through the season, a soccer player has made 15 penalty kicks in 19 attempts. Based on her performance to date, what is the relative frequency probability that she will make her next penalty kick?
Answer:
[tex]\dfrac{15}{19}[/tex]
Step-by-step explanation:
The soccer player so far has made 15 penalty kicks in 19 attempts.
Therefore:
Total Number of trials =19
Number of Successes =15
Therefore, the relative frequency probability that she will make her next penalty kick is:
[tex]=\dfrac{\text{Number of Successes}}{\text{Total Number of Trials}} \\=\dfrac{15}{19}[/tex]
Carpetland salespersons average $8000 per week in sales. Steve Contois, the firm's vice president, proposes a compensation plan with new selling incentives. Steve hopes that the results of a trial selling period will enable him to conclude that the compensation plan increases the average sales per salesperson.a. Develop the appropriate null and alternative hypotheses.: - Select your answer -: - Select your answer -b. In this situation, a Type I error would occur if it was concluded that the new compensation plan provides a population mean weekly sales - Select your answer - when in fact it does not.What are the consequences of making this error
Answer:
The null and alternative hypothesis are:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0[/tex]
where μ1 is the population mean sales with compensation plan, and μ2 is the populatiojn mean sales without compensation plan.
A Type I error is made when a true null hypothesis is rejected. In this case, it would be concluded that the compensation plan increases sales, when in fact it does not (at least, not significantly).
The consequences of this error would be that the compensation plan would have evidence to be implemented in the company when in fact it will not bring the results it is expected to have.
Step-by-step explanation:
This hypothesis test will test the claim that the compensation plan increases the average sales per salesperson. This claim will be stated in the alternative hypothesis, and will state that, with the compensation plan, the sales are significantly higher than without the compensation plan.
The null hypothesis, that Steve wants to falsify, will state that the sales will not differ with or withour compensation plan.
We can write this hypothesis as:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0[/tex]
where μ1 is the population mean sales with compensation plan, and μ2 is the populatiojn mean sales without compensation plan.
A Type I error is made when a true null hypothesis is rejected. In this case, it would be concluded that the compensation plan increases sales, when in fact it does not (at least, not significantly).
The consequences of this error would be that the compensation plan would have evidence to be implemented in the company when in fact it will not bring the results it is expected to have. The sales would be expected to increase due to this implementation, and they will not increase, at least, not for the compensation plan.
What is the solution y=-2x+4 and y=x-2
Answer:
Look below
Step-by-step explanation:
Which equation represents the line that passes through and left-parenthesis 4, StartFraction 7 Over 2 right-parenthesis.?
Answer:
We want a line that passes through the point (4, 7/2)
and we have no other information of this line, so we can not fully find it, but we can find a general line.
We know that a line can be written as:
y = a*x + b.
Now we want that, when x = 4, we must have y = 7/2.
7/2 = a*4 + b
b = -a*4 + 7/2
Then we can write this line as:
y = a*x - a*4 + 7/2.
Where a can take any value, and it is the slope of our line.
Answer:
A
Step-by-step explanation:
Multiply or divide as indicated
x^4•x^-2
Answer:
x^2
Step-by-step explanation:
[tex]x^4\cdot x^{-2}= \\\\x^{4-2}= \\\\x^2[/tex]
Hope this helps!
Answer:
[tex]x^{2}[/tex]
Step-by-step explanation:
[tex]x^4 \times x^{-2}[/tex]
[tex]x^{4+-2}[/tex]
[tex]x^{4-2}[/tex]
[tex]x^{2}[/tex]
What is the area of the trapezoid below? Select one: a. 88 cm2 b. 44√3 cm2 c. 65 cm2 d. 36√3 cm2
Answer: D
Step-by-step explanation:
Since we are not given the height of the trapezoid, we can split this into a triangle and a rectangle. We find the area of each and then add them together. In order to do so, we must use Pythagorean Theorem to find the missing length so that we can find the area.
a²+b²=c²
a²+4²=8²
a²+16=64
a²=48
a=√48
a=4√3
Now that we know the missing length of the triangle, we can find the area of the triangle and the rectangle.
Triangle
A=1/2bh
A=1/2(4)(4√3)
A=8√3
-----------------------------------------------------------------------------------------
Rectangle
A=lw
A=7(4√3)
A=28√3
With our areas, we can add them together.
4√3+28√3=36√3 cm²
we nendndhdhebdbdbdd
Step-by-step explanation:
Joe mama
Pleassssssseeeeee hhheeelllppp
A= -2+(-3)×(-8+4)
-2+(-3)×(-4)
-2+12=10
B=-9+8×7+(-12)
-9+56-12=35
C=8-2= -4
D=8÷2=4
E= -4-35= -39
F=153
You are building a model sailboat. The plans show that the base of the main sail is 9 cm, the bottom acute angle in the sail is 52°, and the distance between the base of the sail and the deck is 2 cm. What is the height of the mast? a. 12.5 cm b. 11.2 cm c. 13.5 cm d. 11.5 cm
Answer:
c. 13.5 cm
Step-by-step explanation:
In the right triangle formed by the main sail.
Using the trigonometric function
[tex]\tan \theta =\dfrac{\text{Opposite}}{\text{Adjacent}} \\\tan 52^\circ =\dfrac{x}{9} \\x=9 \times \tan 52^\circ\\x=11.52$ cm[/tex]
Therefore:
Height of the mast = 2+11.5=13.5 cm
The height of the mast is 13.5 cm.
The 2003 Zagat Restaurant Survey provides food, decor, and service ratings for some of the top restaurants across the United States. For 15 top-ranking restaurants located in Boston, the average price of a dinner, including one drink and tip, was $48.60. You are leaving on a business trip to Boston and will eat dinner at three of these restaurants. Your company will reimburse you for a maximum of $50 per dinner. Business associates familiar with the restaurants have told you that the meal cost at 5 of the restaurants will exceed $50. Suppose that you randomly select three of these restaurants for dinner.
Required:
a. What is the probability that none of the meals will exceed the cost covered by your company?
b. What is the probability that one of the meals will exceed the cost covered by your company?
c. What is the probability that two of the meals will exceed the cost covered by your company?
d. What is the probability that all three of the meals will exceed the cost covered by your company?
Answer:
a. P(x=0)=0.2967
b. P(x=1)=0.4444
c. P(x=2)=0.2219
d. P(x=3)=0.0369
Step-by-step explanation:
The variable X: "number of meals that exceed $50" can be modeled as a binomial random variable, with n=3 (the total number of meals) and p=0.333 (the probability that the chosen restaurant charges mor thena $50).
The probabilty p can be calculated dividing the amount of restaurants that are expected to charge more than $50 (5 restaurants) by the total amount of restaurants from where we can pick (15 restaurants):
[tex]p=\dfrac{5}{15}=0.333[/tex]
Then, we can model the probability that k meals cost more than $50 as:
[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{3}{k} 0.333^{k} 0.667^{3-k}\\\\\\[/tex]
a. We have to calculate P(x=0)
[tex]P(x=0) = \dbinom{3}{0} p^{0}(1-p)^{3}=1*1*0.2967=0.2967\\\\\\[/tex]
b. We have to calculate P(x=1)
[tex]P(x=1) = \dbinom{3}{1} p^{1}(1-p)^{2}=3*0.333*0.4449=0.4444\\\\\\[/tex]
c. We have to calcualte P(x=2)
[tex]P(x=2) = \dbinom{3}{2} p^{2}(1-p)^{1}=3*0.1109*0.667=0.2219\\\\\\[/tex]
d. We have to calculate P(x=3)
[tex]P(x=3) = \dbinom{3}{3} p^{3}(1-p)^{0}=1*0.0369*1=0.0369\\\\\\[/tex]
The measurement of the circumference of a circle is found to be 64 centimeters, with a possible error of 0.9 centimeter. (a) Approximate the percent error in computing the area of the circle. (Round your answer to two decimal places.) 2.81 Correct: Your answer is correct. % (b) Estimate the maximum allowable percent error in measuring the circumference if the error in computing the area cannot exceed 1%. (Round your answer to one decimal place.)
Answer:
(a) 2.81%
(b) 0.5%
Step-by-step explanation:
We have the following information from the statement:
P = 64 + - 0.9
(a) We know that the perimeter is:
P = 2 * pi * r
if we solve for r, we have to:
r = P / 2 * pi
We have that the formula of the area is:
A = pi * r ^ 2
we replace r and we are left with:
A = pi * (P / 2 * pi) ^ 2
A = (P ^ 2) / (4 * pi)
We derive with respect to P, and we are left with:
dA = 2 * P / 4 * pi * dP
We know that P = 64 and dP = 0.9, we replace:
dA = 2 * 64/4 * 3.14 * 0.9
dA = 9.17
The error would come being:
dA / A = 9.17 / (64 ^ 2/4 * 3.14) = 0.02811
In other words, the error would be 2.81%
(b) tell us that dA / A <= 0.01
we replace:
[P * dP / 2 * pi] / [P ^ 2/4 * pi] <= 0.01
solving we have:
2 * dP / P <= 0.01
dP / P <= 0.01 / 2
dP / P <= 0.005
Which means that the answer is 0.5%
We have five samples of data: sample A with 30 successes of 50 cases, sample B with 600 successes of 1000 cases, sample C with 3000 successes of 5000 cases, sample D with 60 successes of 100 cases and sample E with 300 successes of 500 cases. We want to test if the proportion of successes is greater than 0.5. Which sample gives the strongest evidence for the alternative hypothesis?A. AB. BC. CD. DE. E
Answer:
C. with 3000 successes of 5000 cases sample
Step-by-step explanation:
Given that we need to test if the proportion of success is greater than 0.5.
From the given options, we can see that they all have the same proportion which equals to;
Proportion p = 30/50 = 600/1000 = 0.6
p = 0.6
But we can notice that the number of samples in each case is different.
Test statistic z score can be calculated with the formula below;
z = (p^−po)/√{po(1−po)/n}
Where,
z= Test statistics
n = Sample size
po = Null hypothesized value
p^ = Observed proportion
Since all other variables are the same for all the cases except sample size, from the formula for the test statistics we can see that the higher the value of sample size (n) the higher the test statistics (z) and the highest z gives the strongest evidence for the alternative hypothesis. So the option with the highest sample size gives the strongest evidence for the alternative hypothesis.
Therefore, option C with sample size 5000 and proportion 0.6 has the highest sample size. Hence, option C gives the strongest evidence for the alternative hypothesis
1. The Wall Street Journal reported that bachelor’s degree recipients with majors in business average starting salaries of $53,900 in 2012 (The Wall Street Journal, March 17, 2014). The results for a sample of 100 business majors receiving a bachelor’s degree in 2013 showed a mean starting salary of $55,144 with a sample standard deviation of $5,200. Conduct a hypothesis test to determine whether the mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012. Use a = .01 as the level of significance
Answer:
The calculated value t = 4.976 > 2.6264 at 0.01 level of significance
Null hypothesis is rejected
Alternative hypothesis is accepted
The mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012
Step-by-step explanation:
Given Mean of the population μ = $53,900
Given sample size 'n' = 100
Mean of the sample size x⁻ = 55,144
Sample standard deviation 'S' = 5200
Null hypothesis:H₀: There is no difference between the means
Alternative Hypothesis :H₁: The mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012
Test statistic
[tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{55144-53900}{\frac{5200}{\sqrt{100} } }[/tex]
t = 4.976
Degrees of freedom
ν = n-1 = 100-1 =99
t₀.₀₁ = 2.6264
The calculated value t = 4.976 > 2.6264 at 0.01 level of significance
Null hypothesis is rejected
Alternative hypothesis is accepted
Final answer:-
The mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012
Answer:
We conclude that the mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012.
Step-by-step explanation:
We are given that the Wall Street Journal reported that bachelor’s degree recipients with majors in business average starting salaries of $53,900 in 2012.
A sample of 100 business majors receiving a bachelor’s degree in 2013 showed a mean starting salary of $55,144 with a sample standard deviation of $5,200.
Let [tex]\mu[/tex] = mean starting salary for business majors in 2013.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] $53,900 {means that the mean starting salary for business majors in 2013 is smaller than or equal to the mean starting salary in 2012}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $53,900 {means that the mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012}
The test statistics that would be used here One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean starting salary = $55,144
s = sample standard deviation = $5,200
n = sample of business majors = 100
So, the test statistics = [tex]\frac{55,144-53,900}{\frac{5,200}{\sqrt{100} } }[/tex] ~ [tex]t_9_9[/tex]
= 2.392
The value of t-test statistic is 2.392.
Now, at 0.01 significance level the t table gives a critical value of 2.369 at 99 degree of freedom for right-tailed test.
Since our test statistic is more than the critical value of t as 2.392 > 2.369, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012.
A machine produces a part for the automotive industry. 4% of the parts produced were defective in the past, and we believe that the current percentage is not higher. What is the needed sample size for estimating the current percentage of defective parts with the 90% confidence and the 3% margin of error
Answer:
[tex]n=\frac{0.04(1-0.04)}{(\frac{0.03}{1.64})^2}=114.76[/tex]
And rounded up we have that n=115
Step-by-step explanation:
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by [tex]\alpha=1-0.90=0.1[/tex] and [tex]\alpha/2 =0.05[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64[/tex]
Solution to the problem
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
The proportion of defectives is estimated as: [tex]\hat p=0.04[/tex]. And on this case we have that the margin of error is [tex]ME =\pm 0.03[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.04(1-0.04)}{(\frac{0.03}{1.64})^2}=114.76[/tex]
And rounded up we have that n=115
If a/b = c/d, which of the following is not true?
1) ad=bc
2) a/c=b/d
3) a+b/b=c+d/d
4) a/d=c/b
5) b/a=d/c
Answer:
Option 4 is not true
Step-by-step explanation:
[tex]\frac{a}{b}=\frac{c}{d}\\\\[/tex]
1)Cross multiply,
ad = bc
So, true
2) a/ c = b/d also true
3) a+b/b = c+d/d also true
For example:
[tex]\frac{1}{4}=\frac{2}{8}\\\\\frac{1+4}{4}=\frac{2+8}{8}\\\\\frac{5}{4}=\frac{10}{8}\\\\[/tex]
When simplifying 10/8, it is 5/4.
5) b/a = d/c is also true
Jaden had 2 7/16 yards of ribbon. He used 1 3/8 yards of ribbon to make a prize ribbon. How much does he have now?
EASY!
Answer: 17/16 or 1 1/16
Step-by-step explanation:
BRO IT'S ELEMANTARY FRACTIONS!!!!
Graph g(x)=-2|x-5|-4
Answer:
Step-by-step explanation:
Davon is picking out some movies to rent, and he has narrowed down his selections to 4 children's movies, 3 documentaries, 6 comedies, and 5 mysteries. How many different combinations of 9 movies can he rent if he wants all 6 comedies?
Answer:
220
Step-by-step explanation:
There are 6 comedies and 12 non-comedies. He wants all 6 of the comedies, and 3 of the non-comedies.
The number of ways he can choose 6 comedies from 6 is ₆C₆ = 1.
The number of ways he can choose 3 non-comedies from 12 is ₁₂C₃ = 220.
So the total number of combinations is 1 × 220 = 220.
X + 5/7 is less than 1/7
Answer:
x < -4/7
Step-by-step explanation:
X + 5/7 < 1/7
Subtract 5/7 from each side
X + 5/7 -5/7 <1/7-5/7
x < -4/7
The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 2 sin(πt) + 5 cos(πt), where t is measured in seconds.
A) Find the average velocity during each time period.
1) [1, 2]
2) [1, 1.1]
3) [1, 1.01]
4) [1, 1.001]
B) Estimate the instantaneous velocity of the particle when t = 1. cm/s
Answer:
A) 10, -3.73, -6.035, -6.259 . . . cm/s
B) -6.2832 cm/s
Step-by-step explanation:
A) For problems like this, where repeated evaluation of a function is required, I find a graphing calculator or spreadsheet to be an appropriate tool. The attached shows that we defined the position function ...
p(t) = 2sin(πt) +5cos(πt)
and a function for computing the average velocity from t=1. For some time interval ending at t2, the average velocity is ...
Va(t2) = Δp/Δt = (p(t2) -p(1))/(t2 -1)
Then, for example, for t2 = 2, the average velocity on the interval [1, 2] is ...
Va(2) = (p(2) -p(1))/(2 -1) = ((2sin(2π) +5cos(2π)) -(2sin(π) +5cos(π)))/(1)
= (2·0+5·1 -(2·0 +5·(-1)) = 10 . . . . matches the table value for x1 = 2.
Then the average velocity values for the intervals of interest are ...
1) [1, 2] Va = 10
2) [1, 1.1] Va = -3.73
3) [1, 1.01] Va = -6.035
4) [1, 1.001] Va = -6.259
__
B) Sometimes a better estimate is obtained when the interval is centered on the point of interest. Here, we can compute the average velocity on the interval [0.999, 1.001] as a better approximation of the instantaneous velocity at t=1. That value is ...
[0.999, 1.001] Va = -6.283175*
Our estimate of V(1) is -6.2832 cm/s.
The exact value is -2π ≈ -6.2831853... cm/s
__
* This is the average of the Va(0.999) and Va(1.001) values in the table.
If you spin the spinner 11 times, what is the best prediction possible for the number of times it will land on pink?
If we spin the spinner 11 times, 4 is the best prediction possible for the number of times it will land on pink.
To calculate the expected value of a random variable, simply multiply it with the respective probability and sum the respective products.
Given, total number of outcomes=11.
Total number of pink colored spin= 4
Probability of a spin resulting pink color=4/11
Expected number of spins of pink color= [tex]\sum xp(x)[/tex]
=(1×4/11)+(2×4/11)+(3×4/11)+(4×4/11)
=4/11(1+2+3+4)
=40/11
=3.63 ≈ 4
Thus, the best prediction possible for the number of times it will land on pink is 4.
Learn more about expected value, here:
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Incomplete:
Image of spinner is missing in the question, Therefore attaching it below:
Christian Iris and Morgan each get an equal share of 1/2 of pizza which model represent the fraction of the pizza each person gets
Answer:
CICI
Step-by-step explanation: NO cici
Christian, Iris and Morgan each get an equal share of 1/2 of the pizza and the model 1/6 represent the fraction of the pizza each person gets.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
Christian, Iris and Morgan each get an equal share of 1/2 of the pizza.
To find the fraction of the pizza each person gets:
Divide the amount of pizza by the number of people.
There are 3 people and 1/2 pizza.
The fraction of the pizza each person gets
= The amount of pizza / number of people
The fraction of the pizza each person gets
= (1/2) / 3
Simplifying into multiplication,
The fraction of the pizza each person gets = 1/2 x 1/3
The fraction of the pizza each person gets
= 1/(2x3)
= 1/6
Therefore, the model that represents the requirement is 1/6.
To learn more about the division;
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Please answer this correctly
Answer:
9 people
Step-by-step explanation:
37, 39, 41, 46, 61, 63, 69, 77, 80
9 people waited more than 36 minutes.
Cars enter a car wash at a mean rate of 4 cars per half an hour. What is the probability that, in any hour, exactly 5 cars will enter the car wash? Round your answer to four decimal places.
Answer:
The probability that, in any hour, exactly 5 cars will enter the car wash is P(x=5)=0.0920.
Step-by-step explanation:
This can be modeled as a Poisson random variable.
The mean rate is the parameter of the Poisson distribution:
[tex]\lambda=4\;\text{cars/half an hour}=8\;\text{cars/hour}[/tex]
The probability that exactly k cars will enter the car wash can be calculated as:
[tex]P(x=k)=8^{k} \cdot e^{-8}/k![/tex]
Then, the probability that exactly 5 cars will enter the car wash is:
[tex]P(5)=8^{5} \cdot e^{-8}/5!=32768*0.0003/120=0.0920\\\\[/tex]
The probability that, in an hour, exactly 5 cars will enter the car wash will be 0.0920.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1.
Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
The mean rate is found as;
[tex]\rm \lambda =4 \ cars / half \ an \ hour = 8 car / hour[/tex]
The probability that exactly k cars will enter the car wash
[tex]P(x=K) = \frac{8^k e^{-8}}{k\!}\\\\P(x=5) = \frac{8^5 e^{-8}}{5\!}\\\\ P(x=5)=0.0920[/tex]
Hence the probability that, in an hour, exactly 5 cars will enter the car wash will be 0.0920.
To learn more about the probability link is given below.
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Please answer this correctly
Answer:
Pillows:
Blankets:
Pet Beds:
Step-by-step explanation:
18 + 45 + 27 = 90 (there are 90 students)
18 out of 90 = 20%
45 out of 90 = 50%
27 out of 90 = 30%
Hope this helps!
Alice skated 3.4 miles on Monday and 2.6 miles on Wednesday. How much farther did she skate on Monday ?
Answer:
.8 miles further on Monday
Step-by-step explanation:
Take the miles on Monday and subtract the miles on Wednesday
3.4 - 2.6 =.8 miles
Which statement implies that A and B are independent events?
O A. P(B|A)= P(B and A)
OB.P(B|A)= P(B)
P(A)
OC. P(B|A)= P(A)
OD. P(B|A)= P(B)
Answer:
Option B
Step-by-step explanation:
When A and B are independent events:
P(A and B) = P(A) * P(B)
OR
P(A|B) = P(A) * P(B)
What is the equation of the line that goes through (1,-1) and is parallel to y=
3x - 3?
Answer:
y+1=3(x-1), D.
Step-by-step explanation:
Parallel lines have the same slope: Slope should be 3.
y+1=3(x-1)
Blake is going to invest in an account paying an interest rate of 1.5% compounded quarterly. How much would Blake need to invest to the nearest dollar, for the value of the account to reach $910 in 10 years
Answer:
$783.46
Step-by-step explanation:
Compounded interest rate (quarterly) formula: A = P(1 + r/4)^4t
Simply plug in our known variables and solve:
910 = P(1 + 0.015/4)^4(10)
910 = P(1.00375)^40
910 = 1.16151P
P = 783.464
Answer: 783
Step-by-step explanation: