Question

The state of California has a mean annual rainfall of 27.6 inches, whereas the state of New York has a mean annual rainfall of 48.7 inches. Assume the standard deviation for California is 7.4 inches and for New York is 3.1 inches. Find the probability that, for a sample of 45 years of rainfall for California, the mean annual rainfall is at least 29 inches.

Answer 1

Solution :

Given that,

Rainfall for California

mean = = 27.6

standard deviation = = 7.4

n = 45

= 27.6

= / n = 7.4 45 = 1.1031

P (     29 )

= 1 - P (     29 )

= 1 - P ( - /)   ( 27.6 - 29 / 1.1031)

= 1 - P( z   - 1.4 / 1.1031)

= 1 - P ( z -1.27 )   

Using z table

= 1 - 0.1020

= 0.8980

Probability = 0.8980