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

Answer:

$X =4.94\ in$

Step-by-step explanation:

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

the statistic $Z = \frac{X - \mu}{\sigma}$

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.

$2 = \frac{X -\mu}{\sigma}\\\\2\sigma = X - \mu\\\\\2\sigma + \mu = X$

Where:

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