The average student loan debt for college graduates is $25,250. Suppose that that distribution is normal and that the standard deviation is $12,500. Let X = the student loan debt of a randomly selected college graduate. Round all probabilities to 4 decimal places and all dollar answers to the nearest dollar.

A. X ~ N(mean , variance) ~N( 25,250 , 156,250,000 )

B. P(20,000<X<30,000)=0.3108

C.  Low: $20,433.75

High: $30,066.25

Step-by-step explanation:

The question is incomplete.

A. X ~ N( ____ , ____ )

B. Find the probability that the college graduate has between $20,000 and $30,000 in student loan debt.

C. The middle 30% of college graduates' loan debt lies between what two numbers?

Low: $

High: $

We have a normal distribution to represent the average student loan debt for college graduates, with mean $25,250 and standard deviation $12,500.

A) The mean of the distribution is given and is $25,250.

The other parameter is the variance and we can calculate as:

B) To calculate the probability that the debt is between $20,000 and $30,000, we use the z-score for both values:

C) The middle 30% of college graduates' loan debt lies within the interval 15% below the mean and 15% over the mean.

The values can be looked up in a standard normal distribution to know the z-value for this.

The z-value for this interval is z=±0.3853.

Then, we can calculate the lower and upper bound of this interval for the debt's distribution as:

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!