Reference no: EM132892620

Your company is running an audit on the Sleaze Company. Because Sleaze has a bad habit of overcharging its customers, the focus of your audit is on checking whether the billing amount on its invoices are correct. Assume that each invoice is for too high an amount with probability 0.09 and for too low an amount with probability of 0.05 (so that the probability of a correct billing is 0.86). Also, assume that the outcome for any invoice is probabilistically independent of the outcomes for other invoices. Use R or Excel to answer the following questions:

a. If you randomly select 200 of Sleaze's invoices, what is the probability that you will find at least 15 invoices that overcharge the customer? What is the probability that you won't find any that undercharge the customer?

b. Find an integer k such that the probability is at least 0.99 that you will find at least k invoices that overcharge the customer. (Hint: Use trial and error to find k)

Now suppose that when Sleaze overcharges a customer, the distribution of the amount overcharged (expressed as a percentage of the correct billing amount) is normally distributed with mean 15% and standard deviation 4%.

c. What percentage of overbilled customers are charged at least 10% more than they should pay.

d. What percentage of all customers are charged at least 10% more than they should pay?

e. If your auditing company samples 200 randomly chosen invoices, what is the probability that it will find at least five where the customer was overcharged by at least 10%?