One out of every three Americans believes that the U.S government should take "primary responsibility"...

Question

One out of every three Americans believes that the U.S government should take "primary responsibility" for eliminating poverty in the United States. If 30 Americans are selected, find the probability that:

A) Exactly eight (8) will believe that the U.S government should take "primary responsibility" for eliminating poverty. (Calculation required)

B) At least eight (8) will believe that the U.S government should take "primary responsibility" for eliminating poverty.

C) Calculate part b again using Normal Distribution.

Answer 1

Pr(exactly 8 believers)

30 randomly chosen. 1 out of 3 are believers

best estimate, most likely outcome is 30/3 = 10

using a binomial distribution

Pr(8) = 30C8(1/3)^22(2/3)^8 = (30!/8!22!)(2^8/3^30)

mean = np = 30(1/3) = 10

var = npq = np(1-p) =10(2/3) = 20

sd =sqr20 = 2sqr5 = 4.47

approximate the normal with the binomial distribution

(8-10)/2sqr5 =-2/2sqr5 = -1/sqr5 = -sqr5/5 = -.4472 = z score

use z tables or a z calculator

.6726 = 67.26% probability of at least 8 out of 30

Pr(>8) =