Part 1 . A sample of 100 individuals was selected for a focus group to determine

Question

Part 1 . A sample of 100 individuals was selected for a focus group to determine information concerning consumer behavior. Among the questions asked was “Have you noticed our advertisements on TV?” Overall, 67 answered yes. 45 males were interviewed, and 27 males answered yes.

What is the probability that a respondent chosen at random did not notice the advertisement on TV? a.24 b.76 c.22 d.33

What is the probability that a respondent chosen at random is a female and has noticed the advertisement on TV? a.49 b.40 c.66 d.18

Part 2. A restaurant is considering extending their opening hours, either by extending their hours on weeknights or weekends. 85% of the customers surveyed said that they preferred extended hours on weekends. 55% of the customers were male. 80% of the males preferred extended weekend hours.

Given that a randomly selected customer prefers extended weeknight hours, what is the probability the individual is a male? a. 0.733 b 0.165 c. 0.825 d. 0.11

Given that a randomly selected customer is a female, what is the probability the individual prefers extended weekend hours? a. 0.911 b 0.922 c 0.857 d. 0.410

Explanation / Answer

PART 1

We have

We are given 67 said yes out of which 27 were male hence 40 must be female

out of a 100 67 said yes implies 33 said no

if ther are 45 male it implies we have 55 females in the group

We need the probabily of respondent did not notice add

33/100 =0.33

We have to select female who has seen the advertisement

We have 55 females and 40 had seen the ad

40/55= 0.73

Part 2

Prefers extended probability it is a male = 44/85=0.52

Given customer is female

probability that individual prefers extended

=41/45 = 0.911

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