Question

Data accumulated by NOAA shows that the average annual precipitation for St. Louis, MO is 34 inches. If 17.75% of the time, the annual precipitation is more than 40 inches, what is the standard deviation for annual precipitation in St. Louis

Answer 1

Answer:

The standard deviation for annual precipitation in St. Louis is 6.48 inches.

Step-by-step 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:

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

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:

$\mu = 34$

If 17.75% of the time, the annual precipitation is more than 40 inches, what is the standard deviation for annual precipitation in St. Louis

This means that Z when X = 40 has a pvalue of 1-0.1775 = 0.8225. So when X = 40, Z = 0.925.

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

$0.925 = \frac{40 - 34}{\sigma}$

$0.925\sigma = 6$

$\sigma = \frac{6}{0.925}$

$\sigma = 6.48$

The standard deviation for annual precipitation in St. Louis is 6.48 inches.