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Chapter 6: Q. 76 (page 404)

76. Rhubarb Suppose you purchase a bundle of 10bare-root rhubarb plants. The sales clerk tells you that on average you can expect 5%of the plants to die before producing any rhubarb. Assume that the bundle is a random sample of plants. Let Y= the number of plants that die before producing any rhubarb. Use the binomial probability formula to find
P(Y=1). Interpret this result in context.

Short Answer

Expert verified

The chance of getting 1out of 10plants that die before producing any rhubarb is 31.51%.

Step by step solution

01

Given information

An average of 5%of the plants to die before producing any rhubarb. Let Y=the number of plants that die before producing any rhubarb. And to find the value of P(Y=1).

02

Explanation

Given:n=10p=0.05

The Binomial Probability:

P(X=k)=nk×pk×(1−p)n−kP(1)=101×(0.05)1×(0.95)10−1≈0.3151

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Most popular questions from this chapter

18. Life insurance

(a) It would be quite risky for you to insure the life of a 21-year-old friend under the terms of Exercise 14. There is a high probability that your friend would live and you would gain \(1250in premiums. But if he were to die, you would lose almost \)100,000. Explain carefully why selling insurance is not risky for an insurance company that insures many thousands of 21-year-old men.

(b) The risk of an investment is often measured by the standard deviation of the return on the investment. The more variable the return is, the riskier the
investment. We can measure the great risk of insuring a single person’s life in Exercise 14by computing the standard deviation of the income Y that the insurer will receive. Find σY using the distribution and mean found in Exercise 14.

Refer to the previous Check Your Understanding (page 390) about Mrs. Desai's special multiple-choice quiz on binomial distributions. We defined X=the number of Patti's correct guesses.

3. What's the probability that the number of Patti's correct guesses is more than 2standard deviations above the mean? Show your method.

A large auto dealership keeps track of sales and leases agreements made during each hour of the day. Let X= the number of cars sold and Y= the number of cars leased during the first hour of business on a randomly selected Friday. Based on previous records, the probability distributions of Xand Yare as follows:

Define D=X-Y.

The dealership’s manager receives a 500bonus for each car sold and a300 bonus for each car leased. Find the mean and standard deviation of the difference in the manager’s bonus for cars sold and leased. Show your work.

To introduce her class to binomial distributions, Mrs. Desai gives a 10-item, multiple-choice quiz. The catch is, that students must simply guess an answer (A through E) for each question. Mrs. Desai uses her computer's random number generator to produce the answer key so that each possible answer has an equal chance to be chosen. Patti is one of the students in this class.

Let X=the number of Patti's correct guesses.

To get a passing score on the quiz, a student must guess correctly at least 6times. Would you be surprised if Patti earned a passing score? Compute an appropriate probability to support your answer.

Benford’s 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 1to 9. In that case, the first digit Yof a randomly selected expense amount would have the probability distribution shown in the histogram.

(a). Explain why the mean of the random variable Y is located at the solid red line in the figure.

(b) The first digits of randomly selected expense amounts actually follow Benford’s law (Exercise 5). What’s the expected value of the first digit? Explain how this information could be used to detect a fake expense report.

(c) What’s P(Y>6)? According to Benford’s law, what proportion of first digits in the employee’s expense amounts should be greater than 6? How could this information be used to detect a fake expense report?
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