Solve the problem.
-The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 70 inches, and a standard deviation of 10 inches. What is the probability that the mean annual snowfall during 25
Randomly picked years will exceed 72.8 inches?
A) 0.0026
B) 0.4192
C) 0.0808
D) 0.5808

Question

Quizplus · Accepted Answer

The mean of the sample distribution is also 70 inches, but the standard deviation of the sample distribution is 2 inches (10 inches/sqrt(25)). To find the probability that the mean annual snowfall during 25 randomly picked years will exceed 72.8 inches, we need to find the z-score:
z = (72.8 - 70) / 2 = 1.4
Using a standard normal distribution table or calculator, we find the probability of z being greater than 1.4 is approximately 0.0808, which is the answer choice C.

Solve the Problem. -The Amount of Snowfall Falling in a Certain Mountain Range