Question

The depth of the snow at Yellowstone National Park in April at the lower geyser basin was normally distributed with a mean of 3.9 inches and standard deviation of 0.52 inches. What value is two standard deviations above the mean?

Answer 1

`X =4.94\ in`

Explanation:

For a standard normal distribution of mean
`\mu_z = 0` and
`\sigma_z = 1`

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

In this problem we look for the value of X that is 2 standard deviations above the mean.

If there are two standard deviations above the mean, then, in the standard normal distribution, the statistic
`Z = 2`.

Then, we clear X.

`2 = (X -\mu)/(\sigma)\\\\2\sigma = X - \mu\\\\\2\sigma + \mu = X\\\\`

Where:

`\sigma=0.52\\\\\mu=3.9\\\\X = 2(0.52) + 3.9\\\\X =4.94`