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=
`(σ)/(√(n)) =(10)/(√(25)) =2`.

The Z-score is
`Z=( 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`