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 44.5 inches. Assume the standard deviation for California is 6.3 inches and for New York is 8.2 inches. Find the probability that, for a sample of 40 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 = = 6.3

n = 40

= 27.6

₌ / n = 6.3 40 = 0.9961

P (    29 )

= 1 - P (    29 )

= 1 - P ( - /)   ( 27.6 - 29 / 0.9961)

= 1 - P( z   - 1.4 / 0.9961)

= 1 - P ( z -1.40 )   

Using z table

= 1 - 0.0808

= 0.9192

Probability = 0.9192