Question

Imagine that you meet a new friend who is also a beginner, and she can run the 5k in 23.5 minutes. You wonder what percentage of the beginner running population could run the 5k faster than your new friend (that is, what percentage of the population has a time that is less than your new friend?). (Hint: use Appendix B.1 to answer this question! It might help to draw out a normal distribution, find your friend's z score on the distribution, and then figure out what area you're looking for in the z-table from the appendix).

Please explain step by step how to do this

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Answer 1

ANSWER::

Let x be the time in minutes to run distance 5k

We can find the sample mean and standard deviation of the given data set using excel function =AVERAGE( ) and =STDEV.S() respectively.

= 24 and S = 1.7951

We are asked to find P( X < 23.5 )

z = =

z = -0.28

Now we have to look on the z score table for corresponding value in the row -0.2 and across the column 0.08  

it is 0.3897

Answer : 38.97%

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