PLEASE HELP WILL RATE The state of California has a mean ann

PLEASE HELP WILL RATE

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 44.5 inches. Assume the standard deviation for California is 6.3 inches and for New York is 5.6 inches. Find the probability that, for a sample of 45 years of rainfall for California, the mean annual rainfall is at least 25 inches

Solution

let the annual rainfall in california follows normal with mean 23.8 inches and standard deviation 6.3 inches.

let X1,X2,....,X45 be a random sample from this distribution and Xbar be the sample mean annual rainfall.

so sample size=45

so Xbar~N(23.8,6.3²/45)

we need to find P[Xbar>25]=P[(Xbar-23.8)/(6.3*squareroot(45))>(25-23.8)/(6.3*squareroot(45))]=P[Z>1.2777]

=1-P[Z<1.2777]=1-0.899322=0.100678 [answer]