Return Rate of Electronics; What is the probability that exactly 18 of the 24 customers made a return for “no trouble found”?

The fact that customers tend to return purchased goods for any reason is a major frustration for the consumer electronics industry. (C. Lawton, The Wall Street Journal, May 8, 2008) Recently, it was reported that 68% of all returns were for “no trouble found”. Consider that a sample of 24 customers who returned consumer electronics purchases was selected.

Answer the following questions. Round your answers to four decimal digits.

Show that the requirements of binomial probability distribution are satisfied.

What is the probability that exactly 18 of the 24 customers made a return for “no trouble found”?

What is the probability that no more than half of the customers made a return for “no trouble found”?

What is the probability that at least half of the customers made a return for “no trouble found”?

What is the expected number of customers in this sample who made a return for “no trouble found”?

What is the standard deviation of this binomial distribution?

The same study also reported that 27% of all the returns were for “buyer’s remorse”.

What is the probability that none of the 24 customers made a return for “buyer’s remorse”?

What is the probability that 6 or more customers made a return for “buyer’s remorse”?

What is the probability that at most 3 customers made a return for “buyer’s remorse”?

What is the expected number of customers in this sample who made a return for “buyer’s remorse”?

What is the standard deviation of this binomial distribution?

Provide an example scenario of a binomial random variable that is related to your area of work (first, you need to describe your work!) and explain clearly how each requirement for the binomial distribution is satisfied.

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