In a lottery, a player must choose 6 numbers between 1 and 48 inclusive. Six balls are then randomly selectedfrom an urn containing 48 balls numbered from 1 to 48. The random variable X represents the number ofmatching numbers. What are the mean and standard deviation of the random variable X?
A) $\mu _ { X } = 0.750 , \sigma X = 35.992$
B) $\mu _ { X } = 0.750 , \sigma X = 0.810$
C) $\mu _ { X } = 0.125 , \sigma X = 35.992$
D) $\mu _ { X } = 0.125 , \sigma X = 0.810$

Question

In a lottery, a player must choose 6 numbers between 1 and 48 inclusive. Six balls are then randomly selectedfrom an urn containing 48 balls numbered from 1 to 48. The random variable X represents the number ofmatching numbers. What are the mean and standard deviation of the random variable X? 
A) $\mu _ { X } = 0.750 , \sigma X = 35.992$
B) $\mu _ { X } = 0.750 , \sigma X = 0.810$
C) $\mu _ { X } = 0.125 , \sigma X = 35.992$
D) $\mu _ { X } = 0.125 , \sigma X = 0.810$

Quizplus · Accepted Answer

The mean of the hypergeometric distribution is given by $\mu _ { X } = n \frac { M } { N }$ and the standard deviation is given by $\sigma X = \sqrt { n \frac { M } { N } \frac { N - M } { N - 1 } \frac { N - n } { N - 1 } }$. In this case, n = 6, M = 6, and N = 48, so $\mu _ { X } = 6 \frac { 6 } { 48 } = 0.750$ and $\sigma X = \sqrt { 6 \frac { 6 } { 48 } \frac { 48 - 6 } { 48 - 1 } \frac { 48 - 6 } { 48 - 1 } } = 35.992$.

In a Lottery, a Player Must Choose 6 Numbers Between μX=0.750,σX=35.992\mu _ { X } = 0.750 , \sigma X = 35.992μX​=0.750,σX=35.992

In a Lottery, a Player Must Choose 6 Numbers Between $\mu _ { X } = 0.750 , \sigma X = 35.992$