A manufacturer receives a shipment of 170 laptop computers of which 9 are defective. To test the shipment, thequality control engineer randomly selects 10 computers from the shipment and tests them. The randomvariable X represents the number of defective computers in the sample. What are the mean and standarddeviation of the random variable X?
A) $\mu \chi = 0.529 , \sigma \chi = 0.689$
B) $\mu _ { X } = 0.529 , \sigma X = 0.708$
C) $\mu _ { X } = 0.053 , \sigma _ { X } = 0.689$
D) $\mu _ { X } = 0.529 , \sigma X = 0.475$

Question

A manufacturer receives a shipment of 170 laptop computers of which 9 are defective. To test the shipment, thequality control engineer randomly selects 10 computers from the shipment and tests them. The randomvariable X represents the number of defective computers in the sample. What are the mean and standarddeviation of the random variable X? 
A) $\mu \chi = 0.529 , \sigma \chi = 0.689$
B) $\mu _ { X } = 0.529 , \sigma X = 0.708$
C) $\mu _ { X } = 0.053 , \sigma _ { X } = 0.689$
D) $\mu _ { X } = 0.529 , \sigma X = 0.475$

Quizplus · Accepted Answer

The correct answer is A because the mean of a binomial distribution is given by $\mu = np$ and the standard deviation is given by $\sigma = \sqrt{np(1-p)}$. In this case, n = 10, p = 9/170, so $\mu = 10 * 9/170 = 0.529$ and $\sigma = \sqrt{10 * 9/170 * (1 - 9/170)} = 0.689$.

A Manufacturer Receives a Shipment of 170 Laptop Computers of Which