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.

mean=4.44

standard deviation=1.67

Step-by-step 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

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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