A very successful car washing shop has roughly 2.4 million dollar revenue every year. Since this...

A very successful car washing shop has roughly 2.4 million dollar revenue every year. Since this is quite a large amount of money for a car washing shop, the IRS (tax people) wants to check whether this establishment is laundering money (sounds familiar?); however, due to the limited resources, they want to be 95% confident in their decision; thus, they send an investigator to record the daily number of customers and record down how much that each customers have to pay on average for the service. The investigator came back and reported that there are roughly 2,000 customers for the month and each one of them paying roughly 80 dollars on average for the services with a standard deviation of 30 dollars. Given this information, what is the approximate probability that the car washing shop can achieve it current claimed revenue and what would be your conclusion here about the legitimacy of this car washing shop (i.e whether they are laundering money or not)?

Solutions

Expert Solution

Number of customers per year = 2000 * 12 = 24000

Average revenue per customers claimed by shop = 2.4 million / 24000 = 100 dollars

Let be the average revenue per customer in sample of 24000 customers

Standard error of mean = 30 / = 0.1936492

~ N( = 80, = 0.1936492)

Approximate probability that the car washing shop can achieve it current claimed revenue

= P( > 100)

= P(Z > (100 - 80)/0.1936492]

= P[Z > 103.28]

= 0.0000

Since the probability that the revenue of 2.4 million dollar revenue every year (average revenue per customers as $100) is almost zero, we conclude that the claim of car washing shop is not legitimate and provide strong evidence that they are involved in laundering money

orchestra answered 1 year ago

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