Question

In Exercises 61 and 62, a binomial experiment is given. Determine whether you can use a normal distribution to approximate the binomial distribution. If you can, find the mean and standard deviation. If you cannot, explain why.

61. A survey of U.S. adults found that 75% support labeling legislation for genetically modified organisms (GMOs). You randomly select 20 U.S. adults and ask them whether they support labeling legislation for genetically modified organisms (GMOs). (Source: The Harris Poll)

62. A survey of U.S. likely voters found that 11% think Congress is doing a good or excellent job. You randomly select 45 U.S. likely voters and ask them whether they think Congress is doing a good or excellent job. (Source:

Answer 1

To approximate the binomial, np > 5 and n(1-p) > 5

a) 20 * (1 - 0.75) = 5

Mean = n * p = 20 * 0.75 = 15

Standrad deviation = sqrt(n * p * (1 - p)) = sqrt(20 * 0.75 * 0.25) = 1.94

b) 45 * 0.11 = 4.95

So, we can't use approximate.