Q 7.17

According to a recent survey by the National Retail Federation, men spent an average of $135.35 on Valentine's Day gifts (compared with $72.28 for women). Assume the standard deviation for this population is $40 and that it is normally distributed. A random sample of 10 men who celebrate Valentine's Day was selected.

a. Calculate the standard error of the mean.

b. What is the probability that the sample mean will be less than $125?

c. What is the probability that the sample mean will be more than $140?

d. What is the probability that the sample mean will be between $120 and $160?

e. Identify the symmetrical interval that includes 95% of the sample means if the true population mean is $135.35.

Q 7.28

A sample of 150 is drawn from a population with a pro-portion equal to 0.40 and a population size of 400. Determine the probability of observing

a. between 50 and 54 successes.

b. between 55 and 62 successes.

c. between 53 and 70 successes.

Q 7.35

Pike Creek Golf Club currently has 375 members who pay annual dues to play golf on the course. Historical records show that 38% of the members use the course at least once a week during the summer season. To verify this, a random sample of 100 members was selected.

a. Calculate the standard error of the proportion.

b. What is the probability that 32 or more members from the sample used the course at least once a week?

c. What is the probability that between 30 and 40 members from the sample used the course at least once a week?

d. If 50 members from the sample used the course at least once a week, does this support the historical records of course usage?