The table below shows the distribution of ages of workers in a company.
Age/ yr
17 - 21
22 - 26
27 - 31
32 - 36
37 - 41
42 - 46
47 - 51
52 - 56
Workers
12
24
30
37
45
25
10
7
(a) Using an assumed mean of 39, calculate the (i) mean (ii) standard deviation; of the distribution. (b) If a worker is selected at random from the company for an award, what is the probability that he is at most 36 years old?
Explanation
Age(in years)
No of workers
Mid-point (x)
17 - 21
12
19
-20
400
4800
-240
22 - 26
24
24
-15
225
5400
-360
27 - 31
30
29
-10
100
3000
-300
32 - 36
37
34
-5
25
925
-185
37 - 41
45
39
0
0
0
0
42 - 46
25
44
5
25
625
125
47 - 51
10
49
10
100
1000
100
52 - 56
7
54
15
225
1575
105
Total
190
17325
-755
(a)(i) Mean, = = = (ii) Standard deviation = = = (b) Total number of workers = 190 No of workers who are at most 36 years old = 12 + 24 + 30 + 37 = 103 p(award to a person at most 36 years old) = = 0.542
