SCENARIO 1 Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid. The ages of 25 senior citizens were as follows:

60 61 62 63 64 65 66 68 68 69 70 73 73

74 75 76 76 81 81 82 86 87 89 90 92

1.Referring to Scenario 1 calculate the arithmetic mean age of the senior citizens to the nearest hundredth of a year.

2. Referring to Scenario 1, determine the median age of the senior citizens.

3. Referring to Scenario 1 determine the first quartile of the ages of the senior citizens.

4. Referring to Scenario 1 determine the third quartile of the ages of the senior citizens.

5. Referring to Scenario 1, determine the interquartile range of the ages of the senior citizens.

6. Referring to Scenario 1, calculate the standard deviation of the ages of the senior citizens.

SCENARIO 2 The probability that a particular type of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8. You have 2 such alarms in your home and they operate independently.

1. Referring to Scenario 2, the probability that both sound an alarm in the presence of smoke is

2. Referring to Scenario 2, the probability that neither sound an alarm in the presence of smoke is

3. Referring to Scenario 2, the probability that at least one sounds an alarm in the presence of smoke is

SCENARIO 3 The number of column inches of classified advertisements appearing on Mondays in a certain daily newspaper is normally distributed with population mean of 320 and population standard deviation of 20 inches.

1. Referring to Scenario 3, for a randomly chosen Monday, what is the probability there will be less than 340 column inches of classified advertisement?

2. Referring to Scenario 3, for a randomly chosen Monday, what is the probability there will be between 280 and 360 column inches of classified advertisement?

SCENARIO 4 The lifetimes of a certain brand of light bulbs are known to be normally distributed with a mean of 1,600 hours and a standard deviation of 400 hours. A random sample of 64 of these light bulbs is taken.

1. Referring to Scenario 4, what is the probability that the sample mean lifetime is more than 1,550 hours?

2. Referring to Scenario 4, the probability is 0.15 that the sample mean lifetime is more than how many hours?

SCENARIO 5 To become an actuary, it is necessary to pass a series of 10 exams, including the most important one, an exam in probability and statistics. An insurance company wants to estimate the mean score on this exam for actuarial students who have enrolled in a special study program. They take a sample of 8 actuarial students in this program and determine that their scores are: 2, 5, 8, 8, 7, 6, 5, and 7. This sample will be used to calculate a 90% confidence interval for the mean score for actuarial students in the special study program.

1. Referring to Scenario 5, the mean of the sample is __________, while the standard deviation of the sample is __________.

2. Referring to Scenario 5, the confidence interval will be based on __________ degrees of freedom.

3. Referring to Scenario 5, the critical value used in constructing a 90% confidence interval is __________. KEYWORDS: t distribution

4. Referring to Scenario 5, a 90% confidence interval for the mean score of actuarial students in the special program is from __________ to __________. KEYWORDS: t distribution

5. True or False: Referring to Scenario 5, for the confidence interval to be valid, it is necessary that test scores of students in the special study program on the actuarial exam be normally distributed.

6. True or False: Referring to Scenario 5, it is possible that the confidence interval obtained will not contain the mean score for all actuarial students in the special study program.

7. True or False: Referring to Scenario 5, if we use the same sample information to obtain a 95% confidence interval, the resulting interval would be narrower than the one obtained here with 90% confidence.