Question

Find the specified probability, from a table of Normal probabilities. Assume that the necessary conditions and assumptions are met. The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 77 inches, and a standard deviation of 10 inches. What is the probability that the mean annual precipitation during 25 randomly picked years will be less than 79.8 inches?

Answer 1

Given,

$\mu$ = 77 , $\sigma$ = 10

Using central limit theorem,

P($\bar{x}$ < x) = P (Z < x - $\mu$ / ($\sigma$ / sqrt(n) ) )

So,

P( $\bar{x}$ < 79.8 ) = P( Z < 79.8 - 77 / ( 10 / sqrt(25) ))

= P (Z < 1.4)

= 0.9192 (Probability calculated from Z table)