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

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 and standard deviation , the zscore of a measure X is given by:

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:

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.

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

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.