Answer to Question #264738 in Statistics and Probability for King

Question

The School of Business (SOB) careers coordinator has been commissioned by the SOB Board to analyze the starting monthly salaries for freshly employed Bcom graduates. The coordinator selected a random sample of starting monthly salaries of recently freshly employed Bcom. graduates and obtained the following data:-

Salary (Ksh 000)

15-24

25-34

35-44

45-54

55-64

65-74

75-84

No. of graduates

5

10

15

30

20

15

5

Suppose salaries for freshly employed graduates are classified as “poor” and “good” when they fall below Kshs.42, 000 and above Kshs.62, 000 respectively, otherwise as “normal”. What proportion of freshly employed graduates would be expected to fall in each salary category

Answer 1

total number of graduates:

$5+10+15+30+20+15+5=100$

Kshs.42, 000 is in class 35-44 with frequency 15

then number of graduates who are below 42000 in this class:

$\frac{15\cdot(42-35)}{44-35}=11.67=11$ graduates

total number of graduates who are below 42000:

$5+10+11=26$ graduates

proportion of graduates who are below 42000:

$26/100=0.26$

Kshs.62, 000 is in class 55-64 with frequency 20

then number of graduates who are above 62000 in this class:

$\frac{20\cdot(62-55)}{64-55}=15.56=15$ graduates

total number of graduates who are above 62000:

$5+15+15=35$ graduates

proportion of graduates who are above 62000:

$35/100=0.35$