Question

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.

Answer 1

mean=4.44

standard deviation=1.67

Explanation:

The mean and standard deviation for the number of erroneous returns per batch can be calculated using binomial distribution. The binomial distribution is used because

i) There are one of two possible outcomes( error or no error) that can be categorized into success and failure.

ii) The experiment is repeated fix number of times 12.

iii) The probability of success remains constant at each trial i.e. 37%

iv) The trails are independent.The mean and standard deviation of binomial distribution are np and √npq

Here, n=12, p=0.37 and q=1-0.37=0.63

mean=12*0.37=4.44

standard deviation=√12*0.37*0.63=√2.8=1.67