Question

when marques commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 37 minutes and a standard deviation of 4.5 minutes. using the empirical rule, what percentage of his commutes will be between 23.5 and 50.5 minutes?

Explanation:

Step1: Find how many standard deviations from the mean

First, calculate how many standard deviations 23.5 and 50.5 are from the mean (37). For 23.5: $37 - 23.5 = 13.5$, and $13.5\div4.5 = 3$. For 50.5: $50.5 - 37 = 13.5$, and $13.5\div4.5 = 3$. So both values are 3 standard deviations from the mean.

Step2: Apply the empirical rule

The empirical rule (or 68 - 95 - 99.7 rule) states that for a normal distribution, about 99.7% of the data lies within 3 standard deviations of the mean.

Answer:

99.7%