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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, “In the past seven days, how many times did you go to an exercise or fitness center or work out?” 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:

σ2=∑x-μ2Px=0-1.032×0.68+1-1.032×0.05+2-1.032×0.07+3-1.032×0.08+4-1.032×0.05+5-1.032×0.04+6-1.032×0.01+7-1.032×0.02=3.1291

The standard deviation is:

σ=σ2=3.1291≈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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