Question

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 64 randomly picked years will exceed 72.8 inches

Answer 1

Answer:

The probability that the mean annual snowfall during 64 randomly picked years will exceed 72.8 inches is 0.3897

Step-by-step explanation:

Mean =$\mu = 70 inches$

Standard deviation =$\sigma = 10 inches$

We are supposed to find the probability that the mean annual snowfall during 64 randomly picked years will exceed 72.8 inches

We will use z-score formula :

$Z = \frac{x-\mu}{\sigma}\\Z=\frac{72.8-70}{10}\\Z=0.28$

We will use z table

$P(X \geq 72.8)=1-P(X\leq 72.8)=1-0.6103=0.3897$

Hence  the probability that the mean annual snowfall during 64 randomly picked years will exceed 72.8 inches is 0.3897