You plan to conduct a marketing experiment in which students are to taste one of two different brands of soft drink. Their task is to identify correctly the brand they 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 each brand is equally likely to be selected.)

a. What is the probability that the sample will have between 50% and 60% of the identifications correct? The probability is 90% that the sample percentage is contained within what symmetrical limits of the population percentage?

b. What is the probability that the sample percentage of correct identifications is greater than 65%? Which is more likely to occur - more than 60% correct identifications in the sample of 200 or more than 55% correct identifications in a sample of 1,000? Explain.