Question

when rashad commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 34 minutes and a standard deviation of 2.5 minutes. using the empirical rule, determine the interval that represents the middle 95% of his commute times.

Explanation:

Step1: Recall the empirical rule

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

Step2: Calculate the lower bound

The lower bound is $\mu - 2\sigma$, where $\mu = 34$ (mean) and $\sigma=2.5$ (standard deviation).

$$34 - 2\times2.5=34 - 5 = 29$$

Step3: Calculate the upper bound

The upper bound is $\mu + 2\sigma$.

$$34+ 2\times2.5=34 + 5=39$$

Answer:

The interval that represents the middle 95% of his commute times is from 29 minutes to 39 minutes.