Question

Assume that for an ad campaign to be successful, at least 83% of those seeing a television commercial must be able to recall the name of the company featured in the commercial one hour after viewing the commercial. Before distributing an ad campaign nationally, an advertising company plans to show the commercial to a random sample of 22 people. It will also show the same people two additional commercials for different products or businesses. Complete parts a through c. a. Assuming that the advertisement will be successful (83% will be able to recall the name of the company in the ad), what is the expected number of people in the sample who will recall the company featured in the commercial one hour after viewing the three commercials? The expected number of people is ___ . (Type an integer or a decimal. Do not round.) b. Suppose that in the sample of 22 people, 11 were able to recall the name of the company in the commercial one hour after viewing. Based on the premise that the advertising campaign will be successful, what is the probability of 11 or fewer people being able to recall the company name? The probability is __. (Round to four decimal places as needed.)

Answer 1

a. The expected number of people is 18.26. b. The probability is approximately 0.5485.

Step-by-step explanation:

a. The expected number of people in the sample who will recall the company featured in the commercial one hour after viewing the three commercials is 0.83 multiplied by the total number of people in the sample. So, the expected number of people is 0.83 × 22 = 18.26.

b. To find the probability of 11 or fewer people being able to recall the company name, we need to calculate the cumulative binomial probability. We can use the binomial probability formula or a binomial probability calculator to find the probability. Using a calculator, the probability is approximately 0.5485.