Question

1. The recent average starting salary for new college graduates in computer information systems is $47,500. Assume salaries are normally distributed with a standard deviation of $4,500.

1. What is the probability of a new graduate receiving a salary between $45,000 and $50,000?
2. What is the probability of a new graduate getting a starting salary in excess of $55,000?
3. What percent of starting salaries is no more than $42,250?
4. What is the cutoff for the bottom 5% of the salaries?
5. What is the cutoff for the top 3% of the salaries?

Answer 1

a)

P(45000 < Y < 50000) = P(45000 - mean < Y - mean < 50000 - mean)
                  = P((45000 - mean)/SD < (Y - mean)/SD < (50000 - mean)/SD)
                  = P((45000 - mean)/SD < Z < (50000 - mean)/SD)
                  = P((45000 - 47500)/4500< Z < (50000 - 47500)/4500)
                  = P(-0.556 < Z < 0.556)
                  = P(Z < 0.556) - P(Z <-0.556)
                  = 0.422

b)

P(Y > 55000) = P(Y - mean > 55000 - mean)
                  = P( (Y - mean)/SD > (55000 - mean)/SD
                  = P(Z > (55000 - mean)/SD)
                  = P(Z > (55000 - 47500)/4500)
                  = P(Z > 1.667)
                  = 1 - P(Z <= 1.667)
                  = 0.048

c)

P(Y < 42250) = P(Y - mean < 42250 - mean)
                  = P( (Y - mean)/SD < (42250 - mean)/SD
                  = P(Z < (42250 - mean)/SD)
                  = P(Z < (42250 - 47500)/4500)
                  = P(Z < -1.167)
                  = 0.122

d)

P(Z<z) = 0.05

from z table

P(Z<-1.645)=0.05

therefore

y = Z*std dev + mean = -1.645*4500 + 47500 = 40097.5--------------------cutoff

we are allowed to solve four sub parts only