Question

The average starting salary for this year's graduates at a large university (LU) is $20,000 with a standard deviation of $4,000. Furthermore, it is known that the starting salaries are normally distributed. All probabilities should be to four decimal places.

What is the probability that a randomly selected LU graduate will have a starting salary of at least $30,400? Answer

Individuals with starting salaries of less than $15,600 receive a low-income tax break. What percentage of the graduates will receive the tax break? (Round to two decimal places) Answer

What are the minimum and the maximum starting salaries of the middle 95% of the LU graduates? (Round to two decimal places) Minimum Answer, Maximum

Answer 1

µ = 20000

sd = 4000

a)

                                   

                                    = P(Z > 2.6)

                                    = 1 - P(Z < 2.6)

                                    = 1 - 0.9953

                                    = 0.0047

b)

                                

                                 = P(Z < -1.1)

                                 = 0.1357

c) Z score for middle 95% = + Z_0.025 = -1.96, 1.96

Z = (X - µ) / sd

or, X = µ + Z * sd

Minimum answer = 20000 - 1.96 * 4000 = 12160

Maximum answer = 20000 + 1.96 * 4000 = 27840