Question

Statistics from Cornell's Northeast Regional Climate Center indicate that Ithaca, NY, gets an average of 35.4 inches of rain each year, with a standard deviation of 4.2 inches.
During what percentage of years does Ithaca get more than 30 inches of rain?
a. approximately 10.03%
b. approximately 10.95%
c. approximately 90.07%
d. approximately 5.82
e. approximately 94.18%

Answer 1

Answer:

c. approximately 90.07%

Step-by-step explanation:

We need to calculate z-statistic of 30 inches of rain in the normal distribution with an average of 35.4 inches of rain each year, and a standard deviation of 4.2 inches.

z score can be calculated using the formula

z=$\frac{X-M}{s}$ where

• X =30 inches of rain

• M is the average rain in inches (35.4)

• s is the standard deviation (4.2)

using the numbers we get z=$\frac{30-35.4}{4.2}$ ≈ −1,286

Then percentage of years does Ithaca get more than 30 inches of rain is

P(z>-1.286) =1- P(z<-1.286)=1-0.0993 ≈0.9007 or 90.7%