PLEASE SHOW ALL WORK Jumbo shrimp are those that require 10

PLEASE SHOW ALL WORK~

Jumbo shrimp are those that require 10 to 15 shrimp to make a pound. Suppose that the number of jumbo shrimp in a 1-pound bag averages = 12.5 with a standard deviation of s = 1, and forms a normal distribution. What is the probability of randomly picking a sample of n = 25 1-pound bags that average more than M = 13 shrimp per bag?

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    13      
u = mean =    12.5      
n = sample size =    25      
s = standard deviation =    1      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    2.5      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2.5   ) =    0.006209665 [answer]