Question

1. The average amount parents and children spent per child on back-to-school clothes in Autumn 2010 was $527. Assume the standard deviation is $160 and that the amount spent is normally distributed.

What is the probability that the amount spent on a randomly selected child is more than $700? (Round to four decimal places)

What is the probability that the amount spent on a randomly selected child is less than $100? (Round to four decimal places)

What is the probability that the amount spent on a randomly selected child is between $450 and $700? (Round to four decimal places)

What is the probability that the amount spent on a randomly selected child is no more than $300? (Round to four decimal places)

2.

The average stock price for companies making up the S&P 500 is $30, and the standard deviation is $8.20. Assume the stock prices are normally distributed.

What is the probability a company will have a stock price of at least $40? (Round to four decimal places)

What is the probability a company will have a stock price no higher than $20? (Round to four decimal places)

How high does a stock price have to be to put a company in the top 10%? (Round to two decimal places)

3.

Last year the American worker spent an average of 77 hours logged on to the Inter-net while at work. Assume the times are normally distributed and that the standard deviation is 20 hours.

What is the probability a randomly selected worker spent fewer than 50 hours logged on to the Internet? (Round to four decimal places)

What is the probability a worker spent more than 100 hours logged on to the Internet? (Round to four decimal places)

A person is classified as a heavy user if he or she is in the upper 20% of usage. How many hours must a worker have logged on to the Internet to be considered a heavy user? (Round to two decimal places)

4.

According to the Bureau of Labor Statistics, the average weekly pay for a U.S. production worker was $441.84. Assume that available data indicate that production worker wages were normally distributed with a standard deviation of $90.

What is the probability that a worker earned between $400 and $500? (Round to four decimal places)

How much did a production worker have to earn to be in the top 20% of wage earners? (Round to two decimal places)

For a randomly selected production worker, what is the probability the worker earned less than $250 per week? (Round to four decimal places)

5.

The time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. Answer the following questions.

What is the probability of completing the exam in one hour or less? (Round to four decimal places)

What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes? (Round to four decimal places)

Assume that the class has 60 students and that the examination period is 90 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time? (Round to the nearest whole number)

6.

The average ticket price for a Washington Redskins football game was $81.89 for the season. With the additional costs of parking, food. drinks, and souvenirs, the average cost for a family of four to attend a game totaled $442.54. Assume the normal distribution applies and that the standard deviation is $65.

What is the probability that a family of four will spend more than $400? (Round to four decimal places)

What is the probability that a family of four will spend $300 or less? (Round to four decimal places)

What is the probability that a family of four will spend between $400 and $500? (Round to four decimal places)

Answer 1

(c) The normal population has a mean of μ-S527 The standard deviation is ơ $160 The probability that the amount spent on a randomly selected childis between $450 and $700 is X<700-P(45060527 7006027) x- P[450 < 450-521z160 160z100-527 173 160 160 P(-0.48125 <z <1.08125) Pz1.08125)- P(z <-0.48125) 0.860207-0.315169 0.545038 Since, on using excel functiorn normsdist (z) P(450 <X<700)05450 Therefore, probability that the amount spent on a randomly selected child is between $450 and $700 is P(450<X<700)s0.5450 1 (d) The normal population has a mean of $527 The standard deviation is σ $160 The probability that the amount spent on a randomly selected childis no more than $300 is P(X 300)= P(X-μ <300-527 160 160 Pzs-141875) Since, on using excel function 0.077986 P(Xs 300) 00779 Therefore, the probability that the am ount spent on a randomly selected child is no more than $300 is P (X 300) .07791