As many as 20% of all Americans contract influenza each year. A sample of 400 randomly selected Americans is chosen and the number with influenza is recorded. Let X represent the number with influenza in the sample. If X = 75 individuals are found to have influenza, what is the standard deviation of the sampling distribution?

Question

Quizplus · Accepted Answer

First, we need to find the mean (μ) and standard deviation (σ) of the population.

μ = (20/100) * 400 = 80
σ = sqrt(400 * (20/100) * (80/100)) = sqrt(64) = 8

Next, we need to find the standard deviation of the sampling distribution, which is:

σx = σ/sqrt(n) = 8/sqrt(400) = 0.4

Finally, we can use the formula for the standard deviation of the sampling distribution of a proportion:

σp = sqrt(p(1-p)/n)

where p = X/n = 75/400 = 0.1875

σp = sqrt(0.1875(1-0.1875)/400) = 0.0200

Therefore, the answer is C.

As Many as 20% of All Americans Contract Influenza Each