Question

A quality control manager at a local supermarket is investigating broken eggs in the store brand dozen egg cartons. The table below summarizes the data he collected from 150 randomly chosen cartons.

Number of Broken Egg	0	1	2	3	4
Frequency	114	18	13	3	2
Probability, P(x)	.76	.12	.09	.02	.01

What is the standard deviation of the number of broken eggs in a carton? Label your answer with correct statistical notation

What is the expected number of broken eggs in a carton of dozen store brand eggs? Round your answer to two decimal places. Label your answer with correct statistical notation

Answer 1

Expected Number of broken eggs is given by:

E(x) = x*p(x)

X	P(x)	x*P(x)
0	0.76	0
1	0.12	0.12
2	0.09	0.18
3	0.02	0.06
4	0.01	0.04

Expected Value = 0 + 0.18 + 0.12 + 0.06 + 0.04

= 0.4

Thus , there is 0.4 expected number of broken eggs.

Variance = E(x2) - E(x)2

Where E(x2) = x *x* p(x)

Standard deviation 2 = Variance

X	X*p(x)	X*x*p(x)
0	0	0
1	0.12	0.12
2	0.18	0.36
3	0.06	0.18
4	0.04	0.16

E(x2) = 0 + 0.12 + 0.36 + 0.18 + 0.16

= 0.82

Thus , Variance = 0.82 - (0.4)2

   = 0.82 - 0.16

Variance = 0.66

Standard deviation = 0.81

Thus , there is an error of 0.81 broken eggs on an average.

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