Question

The total snowfall per year in Laytonville is normally distributed with mean 99 inches and standard deviation 14 inches. Based on the Empirical Rule, what is the probability that in a randomly selected year, the snowfall was less than 127 inches

Answer 1

Answer: Required probability is 0.9772.

Explanation:

Since we have given that

Mean = 99 inches

Standard deviation = 14 inches

It is normally distributed.

We need to find the probability that in a randomly selected year, the snowfall was less than 127 inches.

As we know that

`z=(X-\mu)/(\sigma)`

So, it becomes,

`P(X<127)\\\\=P(z<(127-99)/(14))\\\\=P(z<2)\\\\=0.9772`

Hence, required probability is 0.9772.