Question

T A pizza delivery takes 30 minutes on average to complete. Given that the standard deviation for this task is 3 minutes and the times for completing this task are normally distributed, what is the probability that on any given day it will take 24 minutes to 36 minutes to complete the task?

Answer 1

95% probability that on any given day it will take 24 minutes to 36 minutes to complete the task.

Explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 30

Standard deviation = 3

What is the probability that on any given day it will take 24 minutes to 36 minutes to complete the task?

24 = 30 - 2*3

So 24 is two standard deviations below the mean

36 = 30 + 2*3

So 36 is two standard deviations above the mean

By the Empirical rule, there is a 95% probability that on any given day it will take 24 minutes to 36 minutes to complete the task.