Question 1

The average amount parents and children spend per child on back-to-school clothes in autumn 2001 was $527 (CNBC, September 5, 2001). Assume the standard deviation is $160 and that the amount spent is normally distributed.

a. What is the probability that the amount spent on a randomly selected child is more than $700?

b. What is the probability that the amount spent on a randomly selected child is less than $100?

c. What is the probability that the amount spent on a randomly selected child is between $450 and $700?

d. What is the probability that the amount spent on a randomly selected child is no more than $300?

Question 2

A person must score in the upper 2% of the population on an IQ test to qualify for membership in Mensa, the international high-IQ society (US Airways Attache, September, 2000). If IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, what score must a person have to qualify for Mensa?

Question 3

The College Board American College Testing Program reported a population mean SAT score of ì = 1020 (The World Almanac 2003). Assume that the population standard deviation is ó = 100.

a. What is the probability that a random sample of 75 students will provide a sample mean SAT score within 10 of the population mean?

b. What is the probability a random sample of 75 students will provide a sample mean SAT score within 20 of the population mean?

Question 4

Nielsen Media Research Reported that the household mean television viewing time during the 8 pm to 11 pm time period is 8.5 hours per week (The World Almanac, 2003). Given a sample size of 300 households and a population standard deviation of ó = 3.5 hours, what is the 95% confidence interval estimate of the mean television viewing time per week during the 8 pm to 11 pm time period?