Distributions, Probability and Confidence Interval

1. A college finds that the data on an achievement test for entering freshmen is mound-shaped and has a mean score of 60 with a standard deviation of 6. If it admits any student who scores 54 or above, approximately what percent of the applicants will be refused admission?
A. 34%
B. 16%
C. 84%
D. 68%

2. The mean time to perform a certain task in Kindergarten follows a mound shaped distribution. The mean time is 10 minutes with a standard deviation of 1 minute. The teachers want to establish a time such that approximately only 2.5% will take longer than this time.
A. The time is 8 minutes.
B. The time is 9 minutes.
C. The time is 11 minutes.
D. The time is 12 minutes.

3. A survey of students at a university revealed the following regarding the gender and the majors of the students:
Major
Gender Accounting Management Finance Total
Male 100 150 50 300
Female 100 50 50 200
Total 200 200 100 500
a. What is the probability of selecting a female student?
b. What is the probability of selecting a finance or an accounting major?
c. What is the probability of selecting a female or an accounting major?
d. What is the probability of selecting an accounting major, given that the person selected is a male?
e. Suppose two students are selected to meet with the president of the university. What is the probability that they are both accounting majors?

4. Find the probability that a standard normal random variable will assume a value between:
a. z = 1.5 and z = .75
b. Greater than 1.25
c. Find a z such that 70% of the area is above that value.

5. The lifetime of a color television picture tube is normally distributed with a mean of 7.8 years and a standard deviation of 3 years.
a. What is the probability that a picture tube will last more than ten years?
b. If the firm guarantees the picture tube for 2 years, what percentage of the television sets sold will have to be replaced because of the picture tube failing?
c. How long should the warranty period be (in years) if they want to replace only 1% of the television picture tubes?

6. In recent years, the use of the telephone as a data collection instrument for opinion polls has been steadily increasing. However, one of the major factors affecting the extent to which the telephone can be used is the refusal rate that is, the percentage of eligible subjects actually contacted who refuse to take part in the poll. Suppose that past records indicate a refusal rate of 20% in a large city. What is the probability that out of 15 people:
a. No one refuses to take part in the poll?
b. Exactly 2 refuse to take part in the poll?
c. At most three refuse to take part in the poll?
d. What is the mean and standard deviation of those who refuse to take part in the poll?

7. We want to estimate the population mean within 5, with a 99 percent level of confidence. The population standard deviation is estimated to be 15. How large a sample is required?

8. Refer to the Real Estate data, which reports information on the homes sold in Denver, Colorado, last year.
a. Develop a 95 percent confidence interval for the mean selling price of the homes.
b. Develop a 95 percent confidence interval for the mean distance the home is from the center of the city.
c. Develop a 95 percent confidence interval for the proportion of homes with an attached garage.

9. The owner of the West End Kwick Fill Gas Station wished to determine the proportion of customers who use a credit card or debit card to pay at the pump. He surveys 100 customers and finds that 80 paid at the pump.
a. Estimate the value of the population proportion.
b. Compute the standard error of the proportion.
c. Develop a 95 percent confidence interval for the population proportion.
d. Interpret your findings.