Last year, the typical college student graduated with $27,700 in debt (The Bosto

Question

Last year, the typical college student graduated with $27,700 in debt (The Boston Globe, May 27, 2012). Let debt among recent college graduates be normally distributed with a standard deviation of $5,000. Use Table 1.

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.)

What is the probability that the average debt of five recent college graduates is more than $30,000?(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.)

Explanation / Answer

Using Central limit theorem the sampling distribution of sample mean is also normal with mean mu=$27700 and standard deviation=sigma/root over n=5000/root over 5=2236.06

a.For X bar=25000, z=(25000-27700)/2236.06

=-1.20

P(X>25000)

=P(z>-1.20)

=1-P(z<-1.20)

=1-0.1151

=0.8849

b. For X bar=30000, z=(30000-27700)/2236.06

=1.02

P(X>30000)

=P(z>1.02)

=1-P(z<1.02)

=1-0.8461

=0.1539

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