Question

The depth of the snow at Yellowstone National Park in April at the lower geyser basin was normally distributed with a mean of 2.6 inches and standard deviation of 0.39 inches.

What value is two standard deviations above the mean?

Answer 1

A value of 3.38 inches is two standard deviations above the mean

Explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

`\mu = 2.6, \sigma = 0.39`

What value is two standard deviations above the mean?

This is X when Z = 2. So

`Z = (X - \mu)/(\sigma)`

`2 = (X - 2.6)/(0.39)`

`X - 2.6 = 0.39*2`

`X = 3.38`

A value of 3.38 inches is two standard deviations above the mean