Question

Need typed answer only. Do not provide hand written solution

The dean has observed for several years and found that the probability distribution of the salary of the alumni's first job after graduation is normal, with a mean of $56k per year and a standard deviation of $4k.

a. What's the probability that the alumni get a salary of $52k or more in their first jobs?

b. What's the change that the alumni get a salary between $40k and $60k?

c. what is the salary range that 95% of the alumni should be belonged to?

Answer 1

Mean = 56

Std Dev = 4

a)

P(x>52) = 1 – P(x<52) = 1 – P (z< (52-56)/4) = 1-P(z<-1)

= 1 - 0.1587 = 0.8413 or 84.13% (using the Z Table)

b)

P(40<x<60) = P(x<60) – P(x<40) = P (z< (60-56)/4) – P (z< (40-56)/4) = P(z<1)-P(z<-4)

~ 0.8413 – 0 = 0.8413 or 84.13%

c)

alpha = 0.05

Z_Critical = 1.95

Hence, 95% CI = Mean +/- Z_Critical * Std Dev = 56 +/- 1.96*4 = {48.16, 63.84}