Question

Apply the 68-95-99.7 rule to answer this question. The annual precipitation for one city is normally distributed with a mean of 72 inches and a standard deviation of 3.5 inches. In 99.7% of the years, the precipitation in this city is between _______ and _______ inches.

Answer 1

Answer:

61.5 and 82.5 inches.

Explanation:

According to the 68-95-99.7 rule, 99.7% means the values have 3 standard deviations

$\mu=72$ = Mean

$\sigma=3.5$ = Standard deviation

$x=\mu+3\sigma\\\Rightarrow 72+3\times 3.5=82.5$

$y=\mu-3\sigma\\\Rightarrow 72-3\times 3.5=61.5$

Hence, the precipitation in the city will be in between 61.5 and 82.5 inches.