Question

A population proportion is 0.5. A sample of size 200 will be taken and the sample proportion will be used to estimate the population proportion. Use z-table.

Round your answers to four decimal places. Do not round intermediate calculations.

a. What is the probability that the sample proportion will be within +/-0.02 of the population proportion?

b. What is the probability that the sample proportion will be within +/-0.07 of the population proportion?

Answer 1

Solution

Given that,

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

a.

= P[(-0.02) /0.0354 < ( - ) / < (0.02) / 0.0354]

= P(-0.56 < z < 0.56)

= P(z < 0.56) - P(z < -0.56)

= 0.7123 - 0.2877

= 0.4246

Probability = 0.4246

b.

= P[(-0.07) /0.0354 < ( - ) / < (0.07 ) / 0.0354]

= P(-1.98 < z < 1.98)

= P(z < 1.98) - P(z < -1.98)

= 0.9761 - 0.0239

= 0.9522

Probability = 0.9522