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 s

Question

3 years ago

11

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 s

tandard deviation of 5 minutes. Using the empirical rule, determine the interval that represents the middle 95% of his commute times.

Mathematics

1 answer:

mario62 [17] · Answer 1 · 2022-06-25T21:14:10+03:00

Answer:

[34,54]

Step-by-step 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]