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

61.5 and 82.5 inches.

Step-by-step 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* 3.5=82.5`

`y=\mu-3\sigma\\\Rightarrow 72-3* 3.5=61.5`

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