Suppose that 20% of the items produced by a production are defective, and a sample of 25 items is selected from the produced items, at random. What is expected number of defective items in the selected 25 items ? What is the standard deviation of defective items in 25 selected items.

Question:

Suppose that 20% of the items produced by a production are defective, and a sample of 25 items is selected from the produced items, at random. What is expected number of defective items in the selected 25 items ? What is the standard deviation of defective items in 25 selected items.

Solution:

Assuming that binomial distribution is valid in this experiment, we have n=25 and p= .20. Therefore, the expected number of defective in a sample of 25 items is given by
E (x) = np = 25 x.2 = 5 defective items.

The variance of defective items is
V(x) = npq = np (1-p) = 25 x.2 x .8 = 4

Therefore, the standard deviation is

√4 = 2

defective items