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: Calculate number of standard - deviations from the mean

First, find the number of standard - deviations for the lower and upper bounds.
For the lower bound $x_1 = 23.5$:
$z_1=\frac{x_1-\mu}{\sigma}=\frac{23.5 - 37}{4.5}=\frac{- 13.5}{4.5}=-3$
For the upper bound $x_2 = 50.5$:
$z_2=\frac{x_2-\mu}{\sigma}=\frac{50.5 - 37}{4.5}=\frac{13.5}{4.5}=3$

Step2: Apply the empirical rule

The empirical rule for a normal distribution states that approximately 99.7% of the data lies within $z=-3$ and $z = 3$ standard - deviations of the mean.

Answer:

99.7%