Question

There were 38 tubes containing exactly 40 Smarties. The observed distribution of yellow beans in these 38 tubes is given in the following table.

Number of yellow beans	0	1	2	3	4	5	6	7	8	≥9
Frequency	0	2	10	6	7	5	2	5	1	0

Calculate the proportions of tubes of 40 Smarties that contain 0, 1, 2, . . . , 8,≥ 9 yellow beans. Give the proportions rounded to three decimal places.

Answer 1

Given is the following frequency distribution of yellow beans in these 38 tubes ,

Number of yellow beans	0	1	2	3	4	5	6	7	8	≥9
Frequency	0	2	10	6	7	5	2	5	1	0

To obtain the corresponding probability distribution of tubes of 40 Smarties that contain 0, 1, 2, . . . , 8,≥ 9 yellow beans,
and is obtained as follows,

Number of Yellow Beans	Proportion of tubes of 40 Smarties
0	0
1	1/38 = 0.026
2	10/38 = 0.263
3	6/38 = 0.158
4	7/38 = 0.184
5	5/38 = 0.132
6	2/38 = 0.053
7	5/38 = 0.132
8	1/38 = 0.026
	0

Answer : Above table is the required corresponding proportions of tube of 40 Smarties