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Homework answers / question archive / A quality controller knows by his experience that 10% of the items he inspects are defective
A quality controller knows by his experience that 10% of the items he inspects are defective. He randomly selects 30 items from the production and wants to inspect them.
a. Calculate the expected number of defective items he is going to find.
b. What are the variance and the standard deviation of the number of defective items that the quality controller is going to find?
Answer:
Given, probability that an item is defective or p = 10% = 0.10
Probability that an item is not defective or 1 - p = 1 - 0.10 = 0.90
Since there are only 2 possibilities that whether an item is defective or not we will use the binomial probability distribution.
30 samples are selected at random, n = 30
a.
Expected number of defective items in a binomial probability distribution is given by = n*p
Let the variable be defined by X
Mean or E(X) = n * p = 30*0.1 = 3
Expected number of defective items = 3
b. Variance and standard deviation of the number of defective items
Variance in a binomial distribution is given by = n*p*(1-p)
Variance or V(X) = n*p*(1-p) = 30*0.1*0.9 = 2.7
The variance of the number of defective items = 2.7
Standard Deviation is calculated as the square root of the variance
Standard Deviation = 
= 
=1.643168
Standard Deviation of number of defective items = 1.643168
