Question

The average annual precipitation for a large Midwest city is 30.85 inches with standard deviation of 3.6 inches. What is the probability that a random selection of 49 years will have mean precipitation higher than 30 inches?

Answer 1

Solution :

Given that,

mean = = 30.85

standard deviation = = 3.6

n=49

= =30.85

= / n = 3.6 / 49 = 0.51

P( >30 ) = 1 - P( <30 )

= 1 - P[( - ) / < (30-30.85) / 0.51]

= 1 - P(z < -1.67)

Using z table

= 1 - 0.0475

probability= 0.9525