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 775 consumers who recognize the Coke brand name.
A) 16, 3.96, is not
B) 16, 16, is
C) 784, 3.96, is
D) 874, 16, is not

Question

Quizplus · Accepted Answer

The mean number of consumers who recognize the Coke brand name is found by multiplying the sample size by the probability of recognition: $800 \times 0.98 = 784$. The standard deviation is calculated using the formula for the standard deviation of a binomial distribution, $\sqrt{n \times p \times (1-p)}$, where $n$ is the sample size, $p$ is the probability of success, and $1-p$ is the probability of failure. Substituting the given values, we get $\sqrt{800 \times 0.98 \times (1-0.98)} = \sqrt{800 \times 0.98 \times 0.02} \approx 3.96$. To determine if 775 is an unusual number of recognitions, we compare it to the range defined by two standard deviations from the mean: $784 \pm 2 \times 3.96$. Since 775 is within this range, it is not considered unusual.

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