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Chapter 6: Q 16. (page 369)

Working outExercise 10 described a large sample survey that asked a sample of people aged 19 to 25 years, 鈥淚n the past seven days, how many times did you go to an exercise or fitness center or work out?鈥� The response Y for a randomly selected survey respondent has the probability distribution shown here. From Exercise 10, E(Y)=1.03. Find the standard deviation of Y. Interpret this value.

Short Answer

Expert verified

The standard deviation is 1.7689.

Step by step solution

01

Step 1. Given information.

The given information is:

02

Step 2. Find and interpret the standard deviation of Y.

The given mean is 1.03.

The predicted value of the squared departure from the mean is known as the variance:

蟽2=鈭�x-渭2Px=0-1.032脳0.68+1-1.032脳0.05+2-1.032脳0.07+3-1.032脳0.08+4-1.032脳0.05+5-1.032脳0.04+6-1.032脳0.01+7-1.032脳0.02=3.1291

The standard deviation is:

蟽=蟽2=3.1291鈮�1.7689


We can see that on average the number of days working out will vary from a mean of 1.03 to 1.7689.

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Most popular questions from this chapter

Easy-start mower Refer to Exercise 92 .

a. Calculate and interpret the mean of T.

b. Calculate and interpret the standard deviation of T.

Red light! Refer to Exercise 84. Calculate and interpret P(Y鈮�7)

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.

Long or short? Put the names of all the students in your statistics class in a hat. Mix up the names, and draw 4 without looking. Let X = the number whose last names have more than six letters.

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this probability.

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