According to the Gallup Organization, 65% of adult Americans are in favor of the death penalty for individuals convicted of murder. Erica selects a random sample of 1000 adult Americans in Will County, Illinois, and finds that 630 of them are in favor of the death penalty for individuals convicted of murder.

(a) Assuming that 65% of adult Americans in Will County are in favor of the death penalty, what is the probability of obtaining a random sample of no more than 630 adult Americans in favor of the death penalty from a sample of size 1000?

(b) Does the result from part

(a) contradict the Gallup Organization’s findings?

Explain.

Transcribed Image Text:

Approach This is a binomial experiment with n = 1000 and p = 0.65. Erica needs to determine the probability of obtaining a random sample of no more than 630 adult Americans who favor the death penalty, assuming 65% of adult Americans favor the death penalty. Computing this probability using the binomial probability formula would be difficult, so Erica will use the normal approximation to the binomial, since np (1 - p) = 1000 (0.65) (10.65) = 227.5 10. Approximate P(X 630) by computing the area under the normal curve to the left of x = 630.5 with x = np = 650 and x = np(1 - p) = 1000 (0.65) (1 - 0.65) 15.083. V1000(0.65) =