Chapter 7, Problem 15PS

You plan to conduct a marketing experiment in which student are to taste one of two different brands of soft drink. Their task is to correctly identify the brand tasted. You select a random sample of 200 students and assume that the students have no ability to distinguish between the two brands. (Hint: if an individual has no ability to distinguish between the two soft drinks, then the two brands are equally likely to be selected.)

a. What is the probability that the sample will have between $50\%$ and $60\%$ of the identifications correct?

b. The probability is $90\%$ that the sample percentage is contained within what symmetrical limits of the population percentage?

c. What is the probability that the sample percentage of correct identifications is greater than $65\%?$

d. Which is more likely to occur–more than $60\%$ correct identifications in the sample of 200 or more than, $50\%$ correct identifications in a sample of $1,000?$ Explain.