When surveyed for brand recognition, 98% of consumers recognize Coke. A new survey of 800 randomly selected consumers is to be conducted. For such a group of 800, determine the mean and standard deviation for the number who recognize the Coke brand name. Considering as unusual a result that differs from the mean by more than two standard deviations, it (___ (is/is not) ___) unusual to get 790 consumers who recognize the Coke brand name.
A) 16, 3.96, is not
B) 16, 16, is
C) 784, 3.96, is not
D) 784, 3.96, is

Question

Quizplus · Accepted Answer

The expected value (mean) for the number of consumers who recognize the Coke brand name is 800 x 0.98 = 784. The standard deviation is the square root of npq, where n = sample size, p = probability of success (0.98), and q = probability of failure (1 - p). Plugging in the values, we get sqrt(800 x 0.98 x 0.02) = 3.96. To check if getting 790 consumers who recognize the Coke brand name is unusual, we need to calculate the z-score: (790 - 784) / 3.96 = 1.52. This is less than 2, so it is not considered unusual. Therefore, the correct answer is C.

When Surveyed for Brand Recognition, 98% of Consumers Recognize Coke