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Chapter 6: Q 13. (page 369)

Get on the boat! A small ferry runs every half hour from one side of a large river to the other. The probability distribution for the random variable Y = money collected on a randomly selected ferry trip is shown here. From Exercise 7, μY=$19.35. Calculate and interpret the standard deviation of Y.

Short Answer

Expert verified

The standard deviation isσ=6.4286.

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 19.35.

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

σ2=∑x-μ2Px=0-19.352×0.02+5-19.352×0.05+10-19.352×0.08+15-19.352×0.16+20-19.352×0.27+25-19.352×0.42=41.3275

The standard deviation is:

σ=41.3275≈6.4286

The amount of money collected on a randomly selected boat journey differs by $6.4286 from the mean amount collected ($19.35) on average.

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