Question

Charles has collected data to find that the total snowfall per year in Reamstown has a normal distribution. Using the Empirical Rule, what is the probability that in a randomly selected year, the snowfall was less than 87 inches if the mean is 72 inches and the standard deviation is 15 inches? Provide the final answer as a percent.

Answer 1

Answer:

0.8413 or 84.13%

Step-by-step explanation:

Given : The mean is 72 inches and the standard deviation is 15 inches

To Find : What is the probability that in a randomly selected year, the snowfall was less than 87 inches

Solution:

Mean = $\mu = 72$

Standard deviation = $\sigma = 15$

Formula : $z=\frac{x-\mu}{\sigma}$

We are supposed to find the probability that in a randomly selected year, the snowfall was less than 87 inches

So, x = 87

Substitute the values in the formula

$z=\frac{87-72}{15}$

$z=1$

Now to find P(z<87) refer the z table

P(Z<87)=0.8413 = 84.13%

So, the probability that in a randomly selected year, the snowfall was less than 87 inches if the mean is 72 inches and the standard deviation is 15 inches is 0.8413 or 84.13%