Calculator Homework #5 - The Central Limit Theorem

Exercise 1 The population mean annual salary for environmental compliance specialists is about $63,500. A random sample of 35 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $60,000? Assume = $6100.

Exercise 2 During a certain week the mean price of gasoline in the New England region was $2.714 per gallon. A random sample of 32 gas stations is drawn from this population. What is the probability that the mean price for the sample was between $2.695 and $2.725 that week? Assume = $0.045.

Exercise 3 The mean height of women in the United States (ages 20 - 29) is 64.3 inches. A random sample of 60 women in this age group is selected. What is the probability that the mean height for the sample is greater than 66 inches? Assume = 2.6 inches.

Exercise 4 An education finance corporation claims that the average credit card debts carried by undergraduates are normally distributed, with a mean of $3173 and a standard deviation of $1120. a) What is the probability that a randomly selected undergraduate, who is a credit card holder, has a credit card balance less than $2700? b) You randomly select 25 undergraduates who are credit card holders. What is the probability that their mean credit card balance is less than $2700?