SOLUTION: Having trouble on a. of the following problem: The State of California has a mean annual rainfall of 23.8 inches, whereas the state of New York has a mean annual rainfall of 46.3

Question 1069815: Having trouble on a. of the following problem:
The State of California has a mean annual rainfall of 23.8 inches, whereas the state of New York has a mean annual rainfall of 46.3 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 45 years of rainfall for California, the mean annual rainfall is at least 25 inches.
a. Show the probability distribution of the sample mean annual rainfall for California.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
the sample distribution has is a t-distribution with 44 df and mean 23.8 and sd=6.3/sqrt(45)=0.939
the probability it is more than 25 inches is t df=48>=(25-23.8)/0.939, or >+1.278.
That probability is 0.1040.
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