Question

A pollster believes that 20% of the voters in a certain area favor a bond issue. If 49 voters are randomly sampled from the large number of voters in this area, approximate the probability that the sampled fraction of voters favoring the bond issue will not differ from the true fraction by more than 0.08. (Round your answer to four decimal places.)

Answer 1

The probability that the sampled fraction of voters favoring the bond issue will not differ from the true fraction by more than 0.08 is 0.7698

Explanation:

Given

n = 64

p = 0.20

X/n -p < 0.06

x-np <0.06n

x-np <0.06 * 64

x-np <3.84

Z score

= (x-np)/sqrt (np(1-p))

= -3.84/ sqrt (64*0.20*0.80)

= -1.20

P (x/n-p<0.06) = P(-1.2<z<1.20) = 1-2*0.1151 = 0.7698