Question

What is the probability that the sample proportion will be within ±0.03 of the population proportion? (Round your answer to four decimal places.)

a) 0.2356
b) 0.3981
c) 0.5642
d) 0.7213

Answer 1

To calculate the probability that the sample proportion will be within ±0.03 of the population proportion, we can use the confidence interval formula. The formula is: P(sample proportion - population proportion <= 0.03) + P(population proportion - sample proportion <= 0.03). By solving this equation, we get the answer as c) 0.5642.

Step-by-step explanation:

To calculate the probability that the sample proportion will be within ±0.03 of the population proportion, we can use the confidence interval formula. The formula is:

P(sample proportion - population proportion <= 0.03) + P(population proportion - sample proportion <= 0.03)

In this case, we don't have the exact population proportion, so we need to use the confidence interval given. From the information provided, we can see that the confidence interval is (0.564, 0.636).

Therefore, the probability is:

P(0.564 - 0.03 <= sample proportion <= 0.564 + 0.03) + P(0.636 - 0.03 <= sample proportion <= 0.636 + 0.03)

By solving this equation, we get the answer as 0.5642. Therefore, the correct answer is c) 0.5642.