Question

Are we influenced to buy a product by an ad we saw on TV? Suppose that the National Infomercial Marketing Association surveyed 50,000 buyers of products. They were interested in how many times a buyer watched a TV infomercial before purchasing the product. Their results are seen below:

Number of times Buyers Saw Infomercial	1	2	3	4	5 or more*
Frequency of Buyers	13500	15500	9000	4500	7500

* This last category was really 5 or more, but we will just treat it as 5 for this example.

1. Use the relative frequencies to compute the probability distribution.
2. Check that the probability distribution is valid.
3. What is the probability that a buyer saw the infomercial at least two times before purchasing the product?
4. What is the probability that the buyer saw the infomercial less than three time before purchasing the product?
5. We will assume that this probability distribution is applicable to the population (all buyers of the product). Find Mu and theta by hand.

Answer 1

Number of times Buyers saw Infomercial	1	2	3	4	5 or more
Frequency of buyers	13500	15500	9000	4500	7500

The relative frequency table is:

x	Frequency	Relative frequency
1	13500	13500/50000 = 0.27
2	15500	15500/50000 = 0.31
3	9000	9000/50000 = 0.18
4	4500	4500/50000 = 0.09
5	7500	7500/50000 = 0.15

Since the sum of the probability is (0.27 + 0.31 + 0.18 + 0.09 + 0.15) = 1 and all the probabilities are greater than 0.

The probability distribution is valid

The probability that a buyer saw the informecial at least two times before purchasing the product

= 0.31 + 0.18 + 0.09 + 0.15 = 0.73

The probability that a buyer saw the informecial less than three time before purchasing the product

= 0.27 + 0.31 = 0.58

Mu = = 2.54

Theta =

= 1.367