Question

1. Assume that the starting salaries for the Class of 2013 college graduates is (rounded, in $1000’s) normally distributed with µ = 45 and σ = 5. (Based on real data.) a. Sketch and label the normal curve. b. In what range must a starting salary be for a graduate to be in (approximately) the highest 16% ? c. In what range must a starting salary be for a graduate to be in (approximately) the lowest .15% ? d. In what range must a starting salary be for a graduate to be in (approximately) the middle 95% ? e. What is the z-score for a graduate who has a starting salary of $42.5? f. What % of 2013 graduates are making less than $42.5?

Answer 1

Assume that the starting salaries for the Class of 2013 college graduates is (rounded, in $1000’s) normally distributed with µ = 45 and σ = 5. (Based on real data.)

1. Sketch and label the normal curve.

b. In what range must a starting salary be for a graduate to be in (approximately) the highest 16% ?

z value for top 16% = 0.994

x = 45+0.994*5=49.97 ( in $1000’s)

or $49970 to maximim

c. In what range must a starting salary be for a graduate to be in (approximately) the lowest .15% ?

z value for lower 15% = -1.036

x = 45-1.036*5=39.82 in ($1000)

Or minimum to $39820

d. In what range must a starting salary be for a graduate to be in (approximately) the middle 95% ?

z value for middle 95% = (-1.96, 1.96)

lower value = 45-1.96*5=35.2 ( in $1000’s) or $35200

upper value = 45+1.96*5=54.8 ( in $1000’s) or $54800

e. What is the z-score for a graduate who has a starting salary of $42.5?

z =(42.5-45)/5 = -0.5

f. What % of 2013 graduates are making less than $42.5?

P( x <42.5) = P( z < -0.5)= 0.3085

The required percentage = 30.85%.