Question

The annual salary of fresh college graduates is thought to be normally distributed with a mean of $45,000 and standard deviation of $8000. Do the following.

(a) What is the z −score of the salary of $55,000? (10 points) (b)

If you randomly select such a graduate, what is the probability that he/she will be earning a salary of $55,000 or less? (Use z −score and Excel function to calculate this) (10 points)

(c) If you randomly select such a graduate, what is the probability that he/she will be earning a salary between $40,000 and $58,000? (Excel function for regular normal distribution to calculate this) (15 points)

Answer 1

Solution:

Given: The annual salary of fresh college graduates is thought to be normally distributed with a mean of $45,000 and standard deviation of $8000.

that is:

Part a) Find the z −score of the salary of $55,000

Part b) If you randomly select such a graduate, what is the probability that he/she will be earning a salary of $55,000 or less?
(Use z −score and Excel function to calculate this)

Use following Excel command to find : P( X ≤ 55000) = P( Z ≤ 1.25) =..........?

=NORM.S.DIST( z , cumulative)

=NORM.S.DIST(1.25,TRUE)

=0.8944

P( X ≤ 55000) = P( Z ≤ 1.25)

P( X ≤ 55000) = 0.8944

Part c) If you randomly select such a graduate, what is the probability that he/she will be earning a salary between $40,000 and $58,000? (Excel function for regular normal distribution to calculate this)

P( 40000 < X < 58000) = ..............?

P( 40000 < X < 58000) =P( X < 58000) - P( X < 40000)

Use following Excel command to find probability:

=NORM.DIST(Upper x , mean , std_dev, cumulative)-NORM.DIST(Lower x , mean , std_dev, cumulative)

=NORM.DIST(58000,45000,8000,TRUE)-NORM.DIST(40000,45000,8000,TRUE)

=0.681933

=0.6819

Thus

P( 40000 < X < 58000) = 0.6819