The number of students taking the SAT has risen to an all-time high of more than 1.5 million (College Board, August 26, 2008). Students are allowed to repeat the test in hopes of improving the score that is sent to college and university admission offices. The number of times the SAT was taken and the number of students are as follows. Number of Times Number of Students 1 721,769 2 601,325 3 166,736 4 22,299 5 6730 a. Let x be a random variable indicating the number of times a student takes the SAT. Show the probability distribution for this random variable. b. What is the probability that a student takes the SAT more than one time? c. What is the probability that a student takes the SAT three or more times? d. What is the expected value of the number of times the SAT is taken? What is your interpretation of the expected value? e. What is the variance and standard deviation for the number of times the SAT is taken?

BuyFind

Statistics for Business & Economic...

12th Edition
David R. Anderson + 4 others
Publisher: South-Western College Pub
ISBN: 9781285846323
BuyFind

Statistics for Business & Economic...

12th Edition
David R. Anderson + 4 others
Publisher: South-Western College Pub
ISBN: 9781285846323

Solutions

Chapter 5.3, Problem 17E
Textbook Problem

The number of students taking the SAT has risen to an all-time high of more than 1.5 million (College Board, August 26, 2008). Students are allowed to repeat the test in hopes of improving the score that is sent to college and university admission offices. The number of times the SAT was taken and the number of students are as follows.

Number of Times Number of Students
1 721,769
2 601,325
3 166,736
4 22,299
5 6730
  1. a. Let x be a random variable indicating the number of times a student takes the SAT. Show the probability distribution for this random variable.
  2. b. What is the probability that a student takes the SAT more than one time?
  3. c. What is the probability that a student takes the SAT three or more times?
  4. d. What is the expected value of the number of times the SAT is taken? What is your interpretation of the expected value?
  5. e. What is the variance and standard deviation for the number of times the SAT is taken?

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Chapter 5 Solutions

Statistics for Business & Economics, Revised (MindTap Course List)
Ch. 5.2 - A technician services mailing machines at...Ch. 5.2 - The two largest cable providers are Comcast Cable...Ch. 5.2 - A psychologist determined that the number of...Ch. 5.2 - The following table is a partial probability...Ch. 5.3 - The following table provides a probability...Ch. 5.3 - The following table provides a probability...Ch. 5.3 - The number of students taking the SAT has risen to...Ch. 5.3 - The American Housing Survey reported the following...Ch. 5.3 - The National Basketball Association (NBA) records...Ch. 5.3 - The probability distribution for damage claims...Ch. 5.3 - The following probability distributions of job...Ch. 5.3 - The demand for a product of Carolina Industries...Ch. 5.3 - The New York City Housing and Vacancy Survey...Ch. 5.3 - The J. R. Ryland Computer Company is considering a...Ch. 5.4 - Given below is a bivariate distribution for the...Ch. 5.4 - A person is interested in constructing a...Ch. 5.4 - The Chamber of Commerce in a Canadian city has...Ch. 5.4 - PortaCom has developed a design for a high-quality...Ch. 5.4 - J.P. Morgan Asset Management publishes information...Ch. 5.4 - In addition to the information in exercise 29 on...Ch. 5.5 - Consider a binomial experiment with two trials and...Ch. 5.5 - Consider a binomial experiment with n = 10 and p =...Ch. 5.5 - Consider a binomial experiment with n = 20 and p =...Ch. 5.5 - A Harris Interactive survey for InterContinental...Ch. 5.5 - In San Francisco, 30% of workers take public...Ch. 5.5 - When a new machine is functioning properly, only...Ch. 5.5 - A Randstad/Harris interactive survey reported that...Ch. 5.5 - Military radar and missile detection systems are...Ch. 5.5 - Twelve of the top 20 finishers in the 2009 PGA...Ch. 5.5 - The Census Bureaus Current Population Survey shows...Ch. 5.5 - A university found that 20% of its students...Ch. 5.5 - According to a survey conducted by TD Ameritrade,...Ch. 5.5 - Twenty-three percent of automobiles are not...Ch. 5.6 - Consider a Poisson distribution with = 3. a....Ch. 5.6 - Consider a Poisson distribution with a mean of two...Ch. 5.6 - Phone calls arrive at the rate of 48 per hour at...Ch. 5.6 - During the period of time that a local university...Ch. 5.6 - More than 50 million guests stay at bed and...Ch. 5.6 - Airline passengers arrive randomly and...Ch. 5.6 - An average of 15 aircraft accidents occur each...Ch. 5.6 - The National Safety Council (NSC) estimates that...Ch. 5.7 - Suppose N = 10 and r = 3. Compute the...Ch. 5.7 - Suppose N = 15 and r = 4. What is the probability...Ch. 5.7 - In a survey conducted by the Gallup Organization,...Ch. 5.7 - Blackjack, or twenty-one as it is frequently...Ch. 5.7 - Axline Computers manufactures personal computers...Ch. 5.7 - The Zagat Restaurant Survey provides food, decor,...Ch. 5.7 - The Troubled Asset Relief Program (TARP), passed...Ch. 5 - The Barrons Big Money Poll asked 131 investment...Ch. 5 - The American Association of Individual Investors...Ch. 5 - The budgeting process for a midwestern college...Ch. 5 - A bookstore at the Hartsfield-Jackson Airport in...Ch. 5 - The Knowles/Armitage (KA) group at Merrill Lynch...Ch. 5 - A survey showed that the average commuter spends...Ch. 5 - A political action group is planning to interview...Ch. 5 - Many companies use a quality control technique...Ch. 5 - The unemployment rate in the state of Arizona is...Ch. 5 - A poll conducted by Zogby International showed...Ch. 5 - Cars arrive at a car wash randomly and...Ch. 5 - A new automated production process averages 1.5...Ch. 5 - A regional director responsible for business...Ch. 5 - Customer arrivals at a bank are random and...Ch. 5 - A deck of playing cards contains 52 cards, four of...Ch. 5 - U.S. News World Reports ranking of Americas best...

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