Question

As reported in Runner's World magazine, the times of the finishers in the new york 10 km run are normally distrubted with a mean of 1.02 hours and a standard deviation of 9 minutes. Let X denote finishing time for the finishers. Then,

A. Find the percentage of finishers with times between 50 and 70 minutes

B. find the percentage of finishers with times between 60 and 75 minutes.

How would I approach the first one. This is what I did for half of the problem

50-1.02/9= 49.9
I don't know where to go from there

Answer 1

You have to find the z-score for both 50 and 70 minutes. Change the 1.02 hours to 61.2 minutes for the mean.

z = (50 -61.2)/9

do the same for the 70 minutes.

go to a standard z-table and find the area between those two values.

Do the same thing for B.

Your mistake was not having the same units. Use minutes with minutes and not hours with minutes.

Answer 2

New York City 10-km Run. As reported in Runner’s World magazine, the times of the finishers in the New York City 10-km run are normally distributed with mean 61 minutes and standard deviation 9 minutes. Let x denote finishing time for finishers in this race.

a. Sketch the distribution of the variable x.
b. Obtain the standardized version, z, of x.
c. Identify and sketch the distribution of z.
d. The percentage of finishers with times between 50 and 70 minutes is equal to the area under the standard normal curve between _______ and _______.
e. The percentage of finishers with times less than 75 minutes is equal to the area under the standard normal curve that lies to the _______ of _______.