Question

Suppose that 55 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 2 percentage points of the actual proportion.

Answer 1

Here the original proportion is
`p=0.55`. The proportion approximately follows normal distribution. Mean is
`\mu=p=0.55`.

Standard deviation is
`image`

The required probability is

`P(0.55-0.02<X<0.55+0.02)=P(0.53<X<0.57)`

`P(0.53<X<0.57)=P((0.53-0.55)/(0.0157)<Z<(0.57-0.55)/(0.0157))`

`P(0.53<X<0.57)=P(-1.274<Z<1.274)`

Using standard normal tables,

`P(0.53<X<0.57)=0.7973`