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=
`(σ)/(√(n)) =(16)/(√(64)) =2`.

The Z-score is
`Z=( 82.8-80)/(2)=1.4`.

Refer to standard normal distribution table.

The required probability is

`P(X<82.8)=P(Z<1.4)=<strong>0.9192</strong>`