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son4ous [18]
3 years ago
14

A population proportion is . A sample of size will be taken and the sample proportion will be used to estimate the population pr

oportion. 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 of the population proportion? b. What is the probability that the sample proportion will be within of the population proportion?
Mathematics
1 answer:
katen-ka-za [31]3 years ago
4 0

Complete Question:

A population proportion is 0.4. A sample of size 200 will be taken and the sample proportion p 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 ±0.03 of the population proportion? b. What is the probability that the sample proportion will be within ±0.08 of the population proportion?

Answer:

A) 0.61351

Step-by-step explanation:

Sample proportion = 0.4

Sample population = 200

A.) proprobaility that sample proportion 'p' is within ±0.03 of population proportion

Statistically:

P(0.4-0.03<p<0.4+0.03)

P[((0.4-0.03)-0.4)/√((0.4)(.6))/200 < z < ((0.4+0.03)-0.4)/√((0.4)(.6))/200

P[-0.03/0.0346410 < z < 0.03/0.0346410

P(−0.866025 < z < 0.866025)

P(z < - 0.8660) - P(z < 0.8660)

0.80675 - 0.19325

= 0.61351

B) proprobaility that sample proportion 'p' is within ±0.08 of population proportion

Statistically:

P(0.4-0.08<p<0.4+0.08)

P[((0.4-0.08)-0.4)/√((0.4)(.6))/200 < z < ((0.4+0.08)-0.4)/√((0.4)(.6))/200

P[-0.08/0.0346410 < z < 0.08/0.0346410

P(−2.3094 < z < 2.3094)

P(z < -2.3094 ) - P(z < 2.3094)

0.98954 - 0.010461

= 0.97908

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