Question

When Isaac 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, determine the interval that represents the middle 95% of his commute times.

Answer 1

Explanation:

68%

Answer 2

[34,54]

Explanation:

-The empirical rule states that the 95% of the sampled observations will fall within two standard deviations of the mean for a normally distributed population.

Where:

• 68% is the first standard deviation
• 95% is the second standard deviation about the mean
• 99.7% is the 3rd standard deviation about the mean.

-Therefore. the middle 95% interval is calculated as:

`CI=\mu+2\sigma\\\\=44\pm 2(5)\\\\=44\pm 10\\\\=[34,54]`

Hence, the interval is [34,54]