A bank has kept record of the checking balances of all its c

A bank has kept record of the checking balances of all its customers and determined that the average daily balance of its customers is $300 with a population standard deviation of $48. A random sample of 144 checking accounts is selected.

a. what is the probability that the sample mean will be at least $296?

Solution

a)

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    296      
u = mean =    300      
n = sample size =    144      
s = standard deviation =    48      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -1      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -1   ) =    0.841344746 [ANSWER]