Need exam prep help for my statistics course The average four-year graduate\'s s

Question

Need exam prep help for my statistics course The average four-year graduate's student loan balance is normally distributed with a mean of $30,000 with a standard deviation of $5,000. Please answer the two questions below about these borrowers. 1. What is the probability that a randomly selected four-year graduate has a student loan balance of less than $27,000? You randomly select two dozen four-year graduates. What is the probability that the mean of their student loan balances is less than $27,000? 2.

Explanation / Answer

Ans:

Given that

mean=30000

standard deviation=5000

1)

z=(27000-30000)/5000=-0.6

P(z<-0.6)=0.2743

2)n=24

standard error of mean=5000/sqrt(24)=1020.62

z=(27000-30000)/1020.62

z=-2.94

P(z<-2.94)=0.0016

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