Question

The mean college loan debt for a 22 year old recent college graduate is approximately normally distributed with a mean debt of $37,000 and a standard deviation of $3000. What is the probability that a 22 year old recent college graduate selected at random will have: ( round all final answers to the nearest tenthousandth).

a) A college loan debt less than $30000

b) A college loan debt greater that $42000

c) A college loan debt between $25000 and $45000

d) what would be the highest 10% college loan debt for a 22 year old recebt college graduate?

Answer 1

Solution: Given that mean = $37000 , s = 3000,

a) P(X < 30000) = P((X-mean)/s < (30000-37000)/3000)
= P(Z < -2.3333)
= 0.0099

b) P(X > 42000) = P(Z > (42000-37000)/3000))
= P(Z > 1.6667)
= 0.0475

c) P(25000 < X < 45000) = P((25000-37000)/3000) < Z < (45000-37000)/3000))
= P(-4 < Z < 2.6667)
= 0.9962

d) for Z = 1.28

X = mean + Z*s = (37000 + 1.28*3000) = 40840