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Chapter 6: Q. 106 (page 431)
Large Counts condition To use a Normal distribution to approximate binomial probabilities, why do we require that both and be a t least ?
the shape of binomial distribution to normal distribution n p and n p 10 is used.
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Roulette Marti decides to keep placing a 1$ bet on number 15 in consecutive spins of a roulette wheel until she wins. On any spin, there's a 1-in-38 chance that the ball will land in the 15 slot.
a. How many spins do you expect it to take for Marti to win?
b. Would you be surprised if Marti won in 3 or fewer spins? Compute an appropriate probability to support your answer.
Taking the train According to New Jersey Transit, the A.M. weekday train from Princeton to New York City has a chance of arriving on time on a randomly selected day. Suppose this claim is true. Choose 6 days at random. Let localid="1654594369074" the number of days on which the train arrives on time.
Ms. Hall gave her class a 10-question multiple-choice quiz.
Letthe number of questions that a randomly selected student in the class answered correctly. The computer output gives information about the probability distribution of . To determine each student鈥檚 grade on the quiz (out of ), Ms. Hall will multiply his or her number of correct answers by and then add . Let the grade of a randomly chosen student in the class.
More easy quiz
a. Find the mean of .
b. Find the range of .
Get on the boat! Refer to Exercise 3. Make a histogram of the probability distribution. Describe its shape.
Exercises 21 and 22 examine how Benford鈥檚 law (Exercise 9) can be used to detect fraud.
Benford鈥檚 law and fraud A not-so-clever employee decided to fake his monthly expense report. He believed that the first digits of his expense amounts should be equally likely to be any of the numbers from 1 to 9. In that case, the first digit Yof a randomly selected expense amount would have the probability distribution shown in the histogram.
(a) What鈥檚 ? According to Benford鈥檚 law (see Exercise 9), what proportion of first digits in the employee鈥檚 expense amounts should be greater than 6? How could this information be used to detect a fake expense report?
(b) Explain why the mean of the random variable Yis located at the solid red line in the figure.
(c) According to Benford鈥檚 law, the expected value of the first digit is . Explain how this information could be used to detect a fake expense report.
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