## Suppose That A Category Of World Class Runners Are Known To Run A Marathon

Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 146 minutes with a standard deviation of 11 minutes. Consider 49 of the races.Let X = the average of the 49 races.Give the distribution of X is X~N (146, 1.57)a) Find the probability that the runner will average between 145 and 148 minutes in these 49 marathons.b) Find the 60th percentile for the average of these 49 marathons.c) Find the median of the average running times.

## Suppose that a category of world class runners are known to run a marathon

Question
Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 146 minutes with a standard deviation of 11 minutes. Consider 49 of the races.

Let X = the average of the 49 races.

Give the distribution of X is X~N (146, 1.57)

a) Find the probability that the runner will average between 145 and 148 minutes in these 49 marathons.

b) Find the 60th percentile for the average of these 49 marathons.

c) Find the median of the average running times.