Question

A survey of the alumni of Monash University revealed that the starting annual salaries of Monash Graduates is normally distributed with a mean of AUD 60,000 and a standard deviation of AUD 15,000.

(a) Find the probability that a randomly selected Monash graduate earns less than AUD 45,000 in the first year of employment. [1 marks]

(b) Find the probability that a randomly selected Monash graduate earns more than AUD 80,000 in the first year of employment. [1 marks]

(c) Find the range for the top 15% all of earners amongst Monash graduates. [2 marks]

Answer 1

Given

=60000

= 15000

(a) when x= 45000

  The probability that a randomly selected Monash graduate earns less than AUD 45,000 in the first year of employment = Area from left to z= -1

= 0.1587 Answer

(b) when x= 80000

The probability that a randomly selected Monash graduate earns more than AUD 80,000 in the first year of employment = 1 - Area from left to z= 1.33

= 1- 0.90878

= 0.09122 Answer

When area of right is 15%

then Z= 1.036

let the minimum earning top 15% is x

so we have

1.036 = x- 60000 / 15000

x= 60000 +15540

x= AUD 75540

maximum when Z= 3.5

so max value = 60000+ 52500 = AUD 112500

The range for the top 15% all of earners amongst Monash graduates=

{ AUD 75540 , AUD 112500} Answer