Question

The Leadville 100, also called the “Race across the sky,” is a 100-mile race through the Colorado Rockies. The race director reports that approximately 5% of runners finish the race in less than 24 hours. Let X be the number of runners who finish the race in less than 24 hours. If 900 runners sign up for the race, what is the standard deviation of X? Assume that the runners’ times are independent of one another.

Answer 1

Solution:

Given:

p = probability of runners finish the race in less than 24 hours = 5% = 0.05

n = Number of  runners sign up for the race = 900

X =  the number of runners who finish the race in less than 24 hours follows a Binomial distribution with parameters n = 900 and p = 0.05

We have to find:the standard deviation of X.

Standard deviation of Binomial random variable is:

( Round answer to specified number of decimal places)