Compute the Mean and Standard Deviation of a Hypergeometric Random Variable
-A manufacturer receives a shipment of 170 laptop computers of which 9 are defective. To test the shipment, the quality control engineer randomly selects 10 computers from the shipment and tests them. The random variable X represents the number of defective computers in the sample. What are the mean and standard deviation of the random variable X
A) $\mu _ { X } = 0.529 , \sigma X = 0.689$
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

Compute the Mean and Standard Deviation of a Hypergeometric Random Variable
-A manufacturer receives a shipment of 170 laptop computers of which 9 are defective. To test the shipment, the quality control engineer randomly selects 10 computers from the shipment and tests them. The random variable X represents the number of defective computers in the sample. What are the mean and standard deviation of the random variable X 
A) $\mu _ { X } = 0.529 , \sigma X = 0.689$
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 mean of a hypergeometric random variable is given by $\mu _ { X } = n \frac { M } { N }$ and the standard deviation is given by $\sigma _ { X } = \sqrt { n \frac { M } { N } \frac { N - M } { N - n } \frac { N - n } { N - 1 } }$. In this case, n = 10, M = 9, and N = 170. Plugging these values into the formulas, we get $\mu _ { X } = 10 \frac { 9 } { 170 } = 0.529$ and $\sigma _ { X } = \sqrt { 10 \frac { 9 } { 170 } \frac { 170 - 9 } { 170 - 10 } \frac { 170 - 10 } { 170 - 1 } } = 0.689$.

Compute the Mean and Standard Deviation of a Hypergeometric Random μX=0.529,σX=0.689\mu _ { X } = 0.529 , \sigma X = 0.689μX​=0.529,σX=0.689

Compute the Mean and Standard Deviation of a Hypergeometric Random $\mu _ { X } = 0.529 , \sigma X = 0.689$