Question

Data accumulated by NOAA shows that the average annual precipitation for St. Louis, MO is 34 inches. If 12% of the time, the annual precipitation is more than 40 inches, what is the standard deviation for annual precipitation in St. Louis?

Answer 1

average annual precipitation for St. Louis, MO is 34 inches

Mean = 34 inches

If 12% of the time, the annual precipitation is more than 40 inches

Let X be annual precipitation for St. Louis, MO

P[ X > 40 ] = 12% = 0.12

P[ X > 40 ] = 0.12

P[ ( X - mean )/sd > ( 40 - mean )/sd ] = 0.12

P[ ( X - 34 )/sd > ( 40 - 34 )/sd ] = 0.12

P[ Z > ( 40 - 34 )/sd ] = 0.12

Also, P[ Z > 1.175 ] = 0.12 ( from table )

Comparing

( 40 - 34 )/sd = 1.175

6/sd = 1.175

sd = 6/1.175

sd = 5.1063

sd = 5.11