A bank has 1500 individual savings accounts with an average

A bank has 1,500 individual savings accounts with an average balance of $3,000 and a standard deviation of $1,200. If the bank takes a random sample of 100 accounts,

(b) how many accounts are expected to be below $2,800?

Solution

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    2800      
u = mean =    3000      
          
s = standard deviation =    1200      
          
Thus,          
          
z = (x - u) / s =    -0.166666667      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -0.166666667   ) =    0.433816167

Thus, out of 100 accounts, we expect 0.433816167*100 = 43.3816167 accounts below $2800.

[ANSWER, 43.3816167]