Question

The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 78 inches, and a standard deviation of 16 inches. what is the probability that the mean annual precipitation during 64 randomly picked years will be less than 80.8 inches?

Answer 1

The sample mean is μ=78, and sample standard deviation is σₓ=σ/
`√(n)`=16/
`√(64)`=2.

The Z-score is
`Z=(80.8-78)/(2) =1.4`.

The required probability

`P(X<80.8)=P(Z<1.4)`

Refer to standard normal distribution table.

`P(Z<1.4)=0.9192`