Needing help on how to solve this Please explain to me The s

Needing help on how to solve this.

Please explain to me.

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 7.4 inches and for New York is 8.2 inches. Find the probability that, for a sample of 35 years of rainfall for California, the mean annual rainfall is at least 25 inches. (See exercise 24 on page 326 of your textbook for a similar problem.)

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    25      
u = mean =    23.8      
n = sample size =    35      
s = standard deviation =    7.4      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    0.959364289      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   0.959364289   ) =    0.168687629 [ANSWER]