FOR INSTRUCTORS USE

1.	a......../7		b....../6		c......./6		d......./6
	........../25
2.	a......../8		b....../7		c......../10		........../25
3.		a......../15		b....../10		........../25
4.		a......../15		b....../10		........../25
TOTAL				........../100

1. Ladies Home Journal (1993) reports that after a long day, when they come home, 45% of dog owners greet their pet before they greet their spouse or children. If ten dog owners are randomly selected,

a. what is the probability that all of the them will greet their dog before they greet their spouse or children?

b. what is the probability that when they come home, at least four of them will greet their pet before they greet their spouse or children?

c. What is the mean number of dog owners out of ten randomly selected who will greet their pet before they greet their spouse or children? What is the standard deviation for this number?

d. Use the normal approximation to find the probability that more than 50% of the dog owners out of 10 will greet their pet before they greet their spouse or children.

2. Interpersonal violence (e.g. rape) generally leads to psychological stress for the victim. Clinical Psychology Review (Vol. 15, 1995) reported on the results of all recently published studies of the relationship between interpersonal violence and psychological stress. The distribution of the time elapsed between the violent incident and the initial signs of stress has a mean of 5.1 years and a standard deviation of 6.1 years. Consider a random sample of 150 victims of interpersonal violence. Let represent the mean time elapsed between violent act and the first sign of stress for the sampled victims.

a. What is the approximate distribution of according to the central limit theorem? (Specify its mean and standard deviation.)

b. Find the probability that exceeds 6 years.

c. What is the probability that is between 4 and 5 years?

2. According to researchers, "One of the primary reason relationships sour is that people stop listening to one another" (USA Today, Aug. 14, 1985). According to the researchers the length of time couples in conflict listen to each other has a mean 8 seconds and a standard deviation of 5 seconds. In a sample of 36 couples in conflict, let represent the mean length of time the couples listen to each other.

a. What is the approximate distribution of according to the central limit theorem? (Specify its mean and standard deviation.)

b. Find the probability that exceeds 9 seconds.

c. What is the probability that will be between 7 and 9 seconds?

3. Medicaid health-assistance program are administered by the individual states, even though part of the funding is federal. The federal government requires that the states perform regular audits in order to ensure that the payments are accurate. One Florida hospital was audited by the Florida Department of Health and Rehabilitative Services (HRS), and a random sample of 25 Medicaid claims was selected. The sample mean of the claims was $34.76. Assume that the population standard deviation was $11.34.

a. Use a 99% confidence interval to estimate the mean of all claims submitted by this hospital.

b. How many claims must be sampled if the HRS wants to estimate the mean size of the hospital's claims to within $1.00(that is a margin of error of ) using a 99% confidence interval?

4. How does lack of sleep affect one's creative ability? In a British study (Sleep, 1989), 12 healthy college students, deprived of one night's sleep, received an array of tests intended to measure thinking time, fluency, flexibility, and originality of thought. Suppose the overall scores of the 12 sleep-deprived students had a mean of 63 and a standard deviation(s) of 17. (Lower scores are associated with a decreased ability to think creatively.)

a. Test the hypothesis that the true mean score of the sleep-deprived subjects is less that 80, the mean score of subjects who received sleep prior to taking the test. Use a=0.05.

b. Give a 95% confidence interval for the true mean score of the sleep-deprived subjects.