The table below shows the number of eggs laid by the chickens in a man's farm in a year.
No of eggs per year
No of chickens
45 - 49
10
50 - 54
36
55 - 59
64
60 - 64
52
65 - 69
28
70 - 74
10
(a) Draw a cumulative frequency curve for the distribution.
(b) Use your graph to find the interquartile range.
(c) If a woman buys a chicken from the farm, what is the probability that the chicken lays at least 60 eggs in a year?
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a)
No of eggs
per year
Class boundaries
Freq
Cum Freq
45 - 49
44.5 - 49.5
10
10
50 - 54
49.5 - 54.5
36
46
55 - 59
54.5 - 59.5
64
110
60 - 64
59.5 - 64.5
52
162
65 - 69
64.5 - 69.5
28
190
70 - 74
69.5 - 74.5
10
200
(b) From the graph, the interquartile range = \(Q_{3} - Q_{1} = 63 - 54 = 9\)
(c) Probability of a chicken laying at least 60 eggs in a year = \(\frac{52 + 28 + 10}{200}\)
= \(\frac{90}{200} = \frac{9}{20}\)
Source: Myschool Past Questions Archive (Record #54454)