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Chapter 6: Q. 7. (page 367)

Get on the boat! Refer to Exercise 3. Find the mean of Y. Interpret this value.

Short Answer

Expert verified

碌=19.35

Step by step solution

01

Step 1. Given information.

Money collected0510152025
Probability 0.020.050.080.160.270.42
02

Step 2. The mean of Y. 

The expected value (or mean) is calculated by multiplying each possibility y by its probability P(Y = y):

碌=危yP(Y=y)=0x0.02+5x0.05+10x0.08+15x0.16+20x0.27+25x0.42碌=19.35

The average amount of money collected on a random ferry trip is $19.35.

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Most popular questions from this chapter

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 P(Y<6)? 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 渭X=3.441. Explain how this information could be used to detect a fake expense report.

Benford鈥檚 law Exercise 9 described how the first digits of numbers in legitimate records often follow a model known as Benford鈥檚 law. Call the first digit of a randomly chosen legitimate record X for short. The probability distribution for X is shown here (note that a first digit can鈥檛 be 0). From Exercise 9, E(X)=3.441. Find the standard deviation of X. Interpret this value.

Each entry in a table of random digits like Table Dhas probability $$ of being a 0 , and the digits are independent of one another. Each line of Table D contains 40 random

digits. The mean and standard deviation of the number of 0 s in a randomly selected line will be approximately

a. mean =0.1, standard deviation =0.05.

b. mean =0.1, standard deviation =0.1.

c. mean =4, standard deviation =0.05.

d. mean =4, standard deviation =1.90.

e. mean =4, standard deviation =3.60.

A balanced scale You have two scales for measuring weights in a chemistry lab. Both scales give answers that vary a bit in repeated weighings of the same item. If the true weight of a compound is 2.00grams (g), the first scale produces readings Xthat have mean 2.000gand standard deviation 0.002g. The second scale鈥檚 readings Yhave mean 2.001gand standard deviation . 0.001gThe readingsXandYare independent. Find the mean and standard deviation of the difference Y-Xbetween the readings. Interpret each value in context.

Ladies Home Journal magazine reported that 66% of all dog owners greet their dog before greeting their spouse or children when they return home at the end of the workday. Assume that this claim is true. Suppose 12 dog owners are selected at random. Let X= the number of owners who greet their dogs first.

a. Explain why it is reasonable to use the binomial distribution for probability calculations involving X.

b. Find the probability that exactly 6 owners in the sample greet their dogs first when returning home from work.

c. In fact, only 4 of the owners in the sample greeted their dogs first. Does this give convincing evidence against the Ladies Home Journal claim? Calculate P(X鈮�4) and use the result to support your answer.
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