Last year the typical college student graduated with 27600 i

Last year, the typical college student graduated with $27,600 in debt (The Boston Globe, May 27, 2012). Let debt among recent college graduates be normally distributed with a standard deviation of $8,000. Use Table 1.

What is the probability that the average debt of five recent college graduates is more than $20,000? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

What is the probability that the average debt of five recent college graduates is more than $25,000? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

Solution

A)

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    20000      
u = mean =    27600      
n = sample size =    5      
s = standard deviation =    8000      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -2.12      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -2.12   ) =    0.982996977 [ANSWER]

***************

b)

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    25000      
u = mean =    27600      
n = sample size =    5      
s = standard deviation =    8000      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -0.73      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -0.73   ) =    0.767304908 [ANSWER]

****************