Question

The times of the runners in a marathon are normally distributed, with a mean of 3 hours and 50 minutes and a standard deviation of 30 minutes. What is the probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes? Use the portion of the standard normal table below to help answer the question.

16%
32%
34%
84%

Answer 1

A 16%

Explanation:

edge 2020

Answer 2

The answer is 16%

Explanation:

Given a mean of 3 hours and 50 minutes and a standard deviation of 30 minutes

so a time less than or equal to 3 hours and 20 minutes is a time 1 standard deviation OUTSIDE from the mean

Use the probability table:

The probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes

= Probability of z being outside 1 SD from mean

= 1 - Probability of z within 1 SD from mean

= 1 - 0.84

= 0.16 or 16%....