1. American women, whose ages are between 18 and 24 have heights that are normally distributed with a mean of 65.5 inches and a standard deviation of 2.5 inches.

a) What is the probability that a group of 16 American women, in that particular age group, have an average height greater than 66 inches?

b) Is it unusual to find an American woman in that age group to be taller than 70.8    inches? Explain.

c) What is the probability of finding an American woman, 18 to 24 years old, to be shorter than 63 inches?

3. In a particular graduate school, the graduating rate is 78%.  If eight graduate students have been randomly selected, find: (Is this a Binomial?)

a) The probability that none of them graduate.

b) The probability that 6 of them graduate.

c) The probability that at least 1 of them graduates.

5. About 10% of the population is left handed.  In a particular school, that will house 100 new students this year, what is the probability that at least 15 of the 100 new students will be left handed?

6. In a class of 50 students, in a recent statistics exam, the mean was 72% and the standard deviation 8%.  What is the probability of randomly selecting a test from this group with a score between 60% and 90%?

7.  In a recent poll, 275 of the 520 residents interviewed opposed a new ordinance. Find a 95% confidence interval.  Does the majority oppose the new ordinance? Explain.

8.  A tried-and-true revenue stream for large cities has been the funds collected from parking meters. A random sample of 75 parking meters yielded a mean of $120.00 per meter with a standard deviation of $ 30.00. Find a 90% confidence interval for the population mean revenue collected.

9.  What test statistic formula do we need for:

a) Population Standard Deviation

b) Population Mean, no sigma.

c) Population proportion.

10.  What are the critical values when finding a confidence interval for the population standard deviation with a sample size of 98.

11.  A random sample of 15 women produced a sample mean of 75.6 beats per minute and a standard deviation of 9 beats per minute.  At a 95% level, test the claim that the population mean heart rate for all women differs from78 beats per minute.  Assume normality.

a)

b)

c)

d)

e)

12. The National Transportation Safety board released, a few years ago, a report indicating that 12% of car accidents involve teenagers.  A sample collected recently of 1000 drivers indicates that 134 teenagers were involved. Test the claim that the number of accidents involving teenagers has increased compared to a few years ago. Use 

a)

b)

c)

d)

e)

13. Given the following set of numbers:

     3, 5, 8, 3, 5, 2, 5, 8, 3, 9, 5, 7, 1, 4, 5, 2, 8, 3, 6, 9, 4, 5, 3, 8, 6, 1, 7, 9, 4, 9, 2, 3, 5.

a) Construct a frequency distribution with 5 classes.

b) Find the mean and standard deviation using the frequency distribution.

c) Find the 5-number summary.

14. A particular employer reports that when applicants are interviewed, 8% of them will fail a lie detector test after a brief interview has been given.  If a group of 6 applicants are interviewed, answer the following questions.

a) Construct a probability distribution.

b) What is the probability that at least 1 of them will fail a lie detector test after a job interview is given?

c) Is it unusual that at least 3 of the 6 applicants will fail a lie detector test? Why?

d) Why is that a normal approximation to this binomial problem does not apply in this case?

15.Consider the following situation: The probability that a person is left-handed is 10%.  If four people are randomly selected and asked if they are left handed, answer the following questions:

a) Does this procedure result in a binomial distribution? If yes, verify the requirements     for this particular experiment.

b)Construct a Probability Distribution Table that includes all possibilities when the 4 people are asked if they are left handed:

  c) Find the sample mean and standard deviation.

  d) Is it usual for the four randomly selected persons to be left-handed? Explain.

16. Heights of men are normally distributed with a mean and standard deviation .What is the probability of randomly selecting a man that is taller than 66 inches but smaller than 72 inches?

19. It is estimated that 32% of adult men believe that their stomach is the least favorite part of their body. What is the probability that 130 or more adult men in a random sample of 300 will say that their stomach is the least favorite part of their body?  Is this a binomial?

20. An admissions director wants to estimate the mean age of all students enrolled at the college. The estimate must be within 0.1 years of the population mean. Assume that the population of ages is normally distributed.

Determine the minimum required sample to construct a 95% C.I. for the population     mean. Assume that the population standard deviation is 12 years.

21.  In crash tests of 38 Honda civic cars, collision repair costs are found to have a distribution that is roughly normal, with the mean of $2086 and a standard deviation of $536. Construct a 95% confidence interval for the mean repair cost in all such vehicle collision.

22.  Weights of men are normally distributed with a mean  and a standard deviation .

    a) What is the probability of randomly selecting a man whose weight is less than 192 lbs?

    b) An elevator manufacturer is worried about the overall weight of an elevator that carries up to 9 adults. If a group of 9 men is randomly selected, what is the probability that their mean weight is less than 192 lbs?

23.  The data on ages (in years) and prices ( in hundreds of dollars) for 8 cars of a specific model are given :

Age              8           3           6           9             2           5             6           3         

Price           45         210       100        33         267        134        109       235       

Find the linear correlation coefficient r. Use an appropriate test to indicate if there is a linear correlation.

24.  Solve the problems by answering: a) State the claim, b) , , c) Test statistic. d) Critical value(s), e) Conclusion and final statement.

A)A sample of 14 cans of brand 1 diet soda has a mean of 23 calories and a standard deviation of 3 calories. Another sample of 16 cans of brand 2 has a mean of 25 calories and a standard deviation of 4 calories. At , test the claim that the mean number of calories per can are different for these two brands of diet soda?

B)Use a 0.05 significance level to test the claim that the mean life span of cell phones is greater than 5 years.  A sample of 27 cell phones gave a sample mean of 4.6 years with a standard deviation of 1.9 years.  Assume normality.

C)A random survey of 436 workers showed that 192 of them said that it is unethical to monitor employee email. When 121 senior-level bosses are surveyed, 40 say that it is unethical to monitor employee email. Use a 0.05 confidence level to test that claim that the proportion of workers is higher than the proportion of senior-level bosses who believe that it is unethical to monitor employee email.

25. Use 24C to construct a 90% C. I. Interpret your results.)