Question

The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 105 ' and a standard deviation of 10 ' what is the probability that the mean annual snowfall during 25 randomly picked years will exceed 107.8 'your answer should be a decimal rounded to the fourth decimal place.

Answer 1

The sample mean is μ=105, and sample standard deviation is σₓ=$\frac{σ}{\sqrt{n}} =\frac{10}{\sqrt{25}} =2$.

The Z-score is $Z=\frac{ 107.8-105}{2}=1.4$.

Refer to standard normal distribution table.

The required probability is

$P(X>107.8)=P(Z>1.4)=1-P(Z<1.4)=0.0808$