Question

question
when mohal commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 31 minutes and a standard deviation of 3.5 minutes. using the empirical rule, determine the interval that represents the middle 99.7% of his commute times.
answer attempt 1 out of 2
(□,□)
submit answer

Explanation:

Step1: Recall empirical rule for 99.7%

For normal distributions, 99.7% of data lies within $\mu \pm 3\sigma$, where $\mu$ is the mean and $\sigma$ is the standard deviation.

Step2: Calculate lower bound

Subtract $3\sigma$ from $\mu$:
$31 - 3\times3.5 = 31 - 10.5 = 20.5$

Step3: Calculate upper bound

Add $3\sigma$ to $\mu$:
$31 + 3\times3.5 = 31 + 10.5 = 41.5$

Answer:

$(20.5, 41.5)$