Question

When Adrian commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 24 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 1

(13.5, 34.5)

Explanation:

The empirical rule states that for a normal distribution, the data will fall within three standard deviations of the mean. 68% of the data falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

Given that mean (µ) = 24 and standard deviation (σ) = 3.5

Using empirical rule, the interval that represents the middle 99.7% = (µ ± 3σ) = (24 ± 3*3.5) = (13.5, 34.5)