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Chapter 6: Q. 24 (page 356)

24. Running a mile A study of 12,000able-bodied male students at the University of Illinois found that their times for the mile run were approximately Normal with mean 7.11minutes and standard deviation 0.74minute. Choose a student at random from this group and call his time for the mile Y. Find P(Y<6) and interpret the result. Follow the
four-step process.

Short Answer

Expert verified

The probability is 0.0668. And there is 6.68%chances that student's run would be less than 6 minutes.

Step by step solution

01

Given information

Normal with mean 7.11minutes and standard deviation 0.74 minute.

02

Explanation

Let's say Xis a random variable that has a normal distribution with a mean of 7.11and a standard deviation of 0.74.

Thez-score is calculated by dividing the value reduced by the mean by the standard deviation:

z=x-μσ
Where, xindicates raw score, μindicates population mean, and σindicates population standard deviation.

P(Y<6)can be calculated as:

P(Y<6)=Py−μσ<9−μσ=PZ<6−7.110.74=P(Z<−1.50)

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