Question

Suppose that 60 percent of the voters in a particular region support a candidate. Find the probability that a sample of 1,000 voters would yield a sample proportion in favor of the candidate within 4 percentage points of the actual proportion.

.0155

.9484

.9952

.9902

Answer 1

We have to find out

P(0.60-0.04<p<0.60+0.04)

P(0.56<p<0.64)

with mean = 60

s.d= ? P(1 - p) 0.60 * 0.40 -= 0.0155 1000

Z value at 0.56

Z = (X - μ) / σ
Z = (0.56 - 0.6) / 0.0155
Z = -2.58065

Z value at 0.56

Z = (X - μ) / σ
Z = (0.64 - 0.6) / 0.0155

Z = 2.58065

P(0.56<p<0.64)=P(-2.58065<z<2.58065) = 0.9951-0.0049=0.9902