Question

question
when abdoulaye commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 45 minutes and a standard deviation of 5 minutes. using the empirical rule, what percentage of his commutes will be between 35 and 55 minutes?

Explanation:

Step1: Calculate z-scores for bounds

First, find how many standard deviations 35 and 55 are from the mean. The z-score formula is $z = \frac{x - \mu}{\sigma}$, where $\mu=45$, $\sigma=5$.
For $x=35$: $z = \frac{35 - 45}{5} = -2$
For $x=55$: $z = \frac{55 - 45}{5} = 2$

Step2: Apply Empirical Rule

The empirical rule states that for a normal distribution, approximately 95% of data lies within 2 standard deviations of the mean.

Answer:

95%