Last year, the typical college student graduated with $28,800 in debt (The Bosto

Question

Last year, the typical college student graduated with $28,800 in debt (The Boston Globe, May 27, 2012). Let debt among recent college graduates be normally distributed with a standard deviation of $6,000.

A.

What is the probability that the average debt of five recent college graduates is more than $28,000?(Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

B.

What is the probability that the average debt of five recent college graduates is more than $33,000?(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 $28,000?(Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

B.

What is the probability that the average debt of five recent college graduates is more than $33,000?(Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

Explanation / Answer

Mean ( u ) =28800
Standard Deviation ( sd )=6000/ Sqrt ( 5 ) = 2683.2816
Number ( n ) = 5
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  

a.
P(X > 28000) = (28000-28800)/6000/ Sqrt ( 5 )
= -800/2683.282= -0.2981
= P ( Z >-0.2981) From Standard Normal Table
= 0.6179                  

b.
P(X > 33000) = (33000-28800)/6000/ Sqrt ( 5 )
= 4200/2683.282= 1.5652
= P ( Z >1.5652) From Standard Normal Table
= 0.0582                  

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