Question

normal distribution - empirical rule
this is the only question in this section.
question
when david commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 44 minutes and a standard deviation of 5 minutes. using the empirical rule, what percentage of his commutes will be between 39 and 49 minutes?
answer attempt 1 out of 2

Explanation:

Step1: Map values to z-scores

First, calculate how many standard deviations 39 and 49 are from the mean:
For 39: $39 = 44 - 5 = \mu - \sigma$
For 49: $49 = 44 + 5 = \mu + \sigma$

Step2: Apply Empirical Rule

The empirical rule states that for a normal distribution, the percentage of data within $\mu \pm \sigma$ is 68%.

Answer:

68%