Question

The amount of snow fall falling in a certain mountain range is normally distributed with a mean of 74 inches, and a standard deviation of 12 inches. what is the probability that the mean annual snowfall during 36 randomly picked years will exceed 76.8 inches?

Answer 1

Given that the sample mean is μ=74 and sample standard deviation σₓ=
`(σ)/( √(n)) =(12)/(√(36)) =2`.

Thge Z- score is
`Z=(76.8-74)/(2) =1.4`.

Now we use the Z-score to calculate the required probability.

Refer to standard normal distribution table.

The required probability is

`P(X>76.8) =P(Z>1.4)=1-P(Z<1.4)=0.0808`