Question

The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 8080 ​inches, and a standard deviation of 1616 inches. what is the probability that the mean annual precipitation during 6464 randomly picked years will be less than 82.882.8 ​inches? round your answer to four decimal places.

Answer 1

The sample mean is μ=80, and sample standard deviation is σₓ=$\frac{σ}{\sqrt{n}} =\frac{16}{\sqrt{64}} =2$.

The Z-score is $Z=\frac{ 82.8-80}{2}=1.4$.

Refer to standard normal distribution table.

The required probability is

$P(X<82.8)=P(Z<1.4)=0.9192$