Probability Problems

Follow the instructions for each problem listed below (from p. 137 of Data-Driven Business Decisions). You will be assessed on the correctness and completeness of your responses.

E2

A market survey is given to 1000 people. One of the questions concerns whether the person recognizes the brand name X. It is known that roughly 60% of people respond yes though this varies to some extent over time, and one of the purposes of the survey is to monitor this.

a) How many of the 1000 people would you expect to recognize brand X? Your answer should not be a single number!

b) Based on your answer to (a), how uncertain and unreliable is the proportion of people who recognize brand X?

c) If a particular survey gave the result of 62% recognition and then a month later the proportion had dropped to 57%, would you be convinced that brand recognition is really decreasing?

E3

You survey 500 customers on whether or not they recognize your brand. On the basis of historical norms you expect 35% or 175 to recognize your brand. But you have been spending more money than usual on advertising. How many more than 175 would start to convince you that the extra money had been worth the expense?