Question

The typical college student graduates with $27,100 in debt (The Boston Globe, May 27, 2012). Let debt among recent college graduates be normally distributed with a standard deviation of $5,000. [You may find it useful to reference the z table.] a. What is the probability that the average debt of two recent college graduates is more than $27,000? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.) b. What is the probability that the average debt of two recent college graduates is more than $32,000? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

Answer 1

Solution :

Given that ,

mean = = 27100

standard deviation = = 5000

a)

P(x > 27000) = 1 - P(x < 27000)

= 1 - P((x - ) / < (27000-27100) /5000 )

= 1 - P(z < -0.02)

= 1 - 0.4920   

= 0.5080

Probability = 0.5080

b)

P(x > 32000) = 1 - P(x <32000)

= 1 - P((x - ) / < (32000-27100) /5000 )

= 1 - P(z < 0.98)

= 1 - 0.8365

= 0.1635

Probability = 0.1635