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/$\sqrt{n}$=16/$\sqrt{64}$=2.

The Z-score is $Z=\frac{80.8-78}{2} =1.4$.

The required probability

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

Refer to standard normal distribution table.

$P(Z<1.4)=0.9192$