Question

The population proportion is 0.50. A sample of size 200 will be taken and the sample proportion p will be used to estimate the population proportion. (Round your answers to four decimal places.) (a) What is the probability that the sample proportion will be within ±0.03 of the population proportion? (b) What is the probability that the sample proportion will be within ±0.05 of the population proportion?

Answer 1

Solution

Given that,

=  [p ( 1 - p ) / n] = [(0.50 * 0.5) / 200] = 0.0354

(a)

= P[(-0.03) /0.0354 < ( - ) / < (0.03) / 0.0354]

= P(-0.85 < z < 0.85)

= P(z < 0.85) - P(z < -0.85)

= 0.8023 - 0.1977

= 0.6046

Probability = 0.6046

(b)

= P[(-0.05) /0.0354 < ( - ) / < (0.05) / 0.0354]

= P(-1.41 < z < 1.41)

= P(z < 1.41) - P(z < -1.41)

= 0.9207 - 0.0793

= 0.8414

Probability = 0.8414