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**STATISTICS PAPER -SOLUTIONS**

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1. Create a sample space if you roll a die (one dice with six sides) two times. List all the possible pairs of numbers or outcomes .

a. Find the probability of Event A = “No fives” __________

b. Find the probability of Event B = “Exactly one three” __________

c. Find the probability of Event C = “The two dice sum to 9” __________

d. Find the probability of Event D = “ No odd numbers” __________

2. Suppose that voting in municipal elections is being studied and that the accompanying table describes the probability distribution for four randomly selected people, where *x* is the number that voted in the last election.

*x* P(*x*)

0 0.24

1 ?

2 0.24

3 0.16

4 0.03

a. Find the probability that 1 person voted in the last election so that this is a valid probability distribution .

b. What is the expected value and standard deviation for the probability distribution ?

μ = _______

σ = _______

c. Interpret the meaning of the expected value in terms of this problem .

d. What is the probability that at more than 1 person voted in the last election ?

__________

3. A quiz consists of 25 multiple-choice questions, each with four possible answers. Only one of the choices is correct. Include calculator functions.

a. What requirements are met to make this a binomial experiment? Be specific relating to this scenario.

b. Find the probability of getting exactly 10 questions correct by guessing on the quiz . _________

c. Find the probability of getting at least two questions correct by guessing on the quiz . __________

d. Find the mean and standard deviation for this problem .

Mean___________

Standard deviation__________

e. Use the maximum usual value to determine if it would be unusual to get 15 out of 25 correct (passing grade) on the test if you guessed on the questions? Why or why not .

4. Sccrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 30 months before certain electronic components deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 7 months, and the distribution of lifetimes is normal.

a. If Accrotime guarantees a full refund on any defective watch for up to 2 years after purchase, what percentage of total production will the company expect to replace? Use correct notation, draw a picture, and indicate the calculator function used for full credit

b. If Accrotime does not want to make refunds on more than 10% of the watches it makes, how long should the guarantee period be (to the nearest month)? Show all work .

______________

5. According to the Opinion Research Corporation, the time men spend in the shower follows a normal distribution with a mean of 11.4 minutes and a standard deviation of 2.1 minutes.

a. Based on this model, find the probability of men that spend less than 14 minutes in the shower? Use correct notation, draw a picture, and indicate the calculator function used for full credit

__________

b. What is the minimum time the slowest 5% spend in the shower? Draw a picture and indicate the calculator function used for full credit

c. If five men are randomly selected, find the probability that their mean time they spend in the shower is greater than 13 minutes. Use correct notation, draw a picture, and indicate the calculator function used for full credit .

6. Scores on the quantitative Graduate Record Exam (GRE) have a mean of 584 and a standard deviation of 151. Assume the scores are normally distributed.

Suppose a graduate school requires (among other qualifications) that applicants score at or above the 90^{th} percentile on the GRE quantitative exam. What score is required? Be sure to include a picture and the calculator function

______________

7. Please refer to the data collected from our statistics classes (summary sheets). GPAs for the class were recorded for both male and female students:

a. Find a 90% confidence interval for the mean GPA for male students. Interpret the interval.

b. Find a 90% confidence interval for the mean GPA for female students. Interpret the interval.

c. Compare the intervals for males and females. Does there appear to be a difference in GPAs for the genders? Why or why not?

8. College is contemplating switching from the quarter system to a semester system. The administration conducts a survey of a random sample of 400 students and finds that 240 of them prefer to remain on the quarter system.

a. Find a 95% confidence interval for the true proportion of all students who would prefer to remain on the quarter system. What is the margin of error?

b. Does the interval you computed in part (a) provide convincing evidence that a majority of all students prefer to remain on the quarter system? Explain.

9. Suppose that, in the population of pregnant women who experience no complications, the length of a pregnancy is normally distributed. A researcher suspects that women who work outside the home during the entire time of their pregnancy tend to have pregnancies that are shorter, on average, than those who do not work outside the home during their pregnancies.

A random sample of 15 of each type of pregnancy are obtained:

Work outside the home: n = 15, mean days of pregnancy is 262.8 and standard deviation of 11.2 days.

Do not work outside the home: n = 15, mean days of pregnancy is 273 and standard deviation of 10.8 days.

a. Construct a 98% confidence interval for the mean days of pregnancy for women who work outside the home. What is the margin of error?

b. Construct a 98% confidence interval for the mean days of pregnancy for women who do not work outside the home. What is the margin of error?

c. From the confidence intervals, can you conclude there is a difference in mean days of pregnancy?

10. A random sample of 948 adult Americans was asked, “Do you think televisions are a necessity or a luxury you could do without?” Of the 948, 52% indicated that televisions are a luxury they could do without.

a. Find a 95% confidence interval for the population proportion of adult Americans who believe that televisions are a luxury they could do without. Interpret the interval.

b. Is it likely the supermajority (more than 60%) of adult Americans believe that televisions are a luxury they could do without? Why or why not?

**STATISTICS PAPER -SOLUTIONS**

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- Submitted On 20 Apr, 2017 02:56:46

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