Of all individual tax returns,37 percent include errors made by the taxpayer.If IRS examiners are assigned randomly selected returns in batches of 12,find the mean and standard deviation for the number of erroneous returns per batch.
A) $\mu = 2.80 , \sigma = 1.67$
B) $\mu = 4.44 , \sigma = 1.67$
C) $\mu = 4.44 , \sigma = 2.80$
D) $\mu = 7.56 , \sigma = 2.80$

Question

Quizplus · Accepted Answer

The number of erroneous returns in a batch of 12 follows a binomial distribution with parameters n=12 and p=0.37. 
The mean of a binomial distribution is μ = np, so μ = 12 x 0.37 = 4.44. 
The standard deviation of a binomial distribution is σ = sqrt(np(1-p)), so σ = sqrt(12 x 0.37 x 0.63) = 1.67. 
Therefore, the best choice is B, with μ = 4.44 and σ = 1.67.

Of All Individual Tax Returns,37 Percent Include Errors Made by the Taxpayer.If