Question

A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the true proportion is 0.05

.

If 299
are sampled, what is the probability that the sample proportion will be less than 0.06
? Round your answer to four decimal places.

Answer 1

Using a standard normal distribution table or calculator, the probability is approximately 0.5307 (rounded to 4 decimal places).

Step-by-step explanation:

To answer this question, we can use the formula for the standard error of the sample proportion:

SE(p) = sqrt((p * (1 - p)) / n) { where p is the population proportion and n is the sample size.

In this case, the population proportion is 0.05 and the sample size is 299.

Calculating the standard error:

SE(p) = sqrt((0.05 * (1 - 0.05)) / 299)

= 0.0146 (rounded to 4 decimal places)

Next, we can calculate the z-score for the given sample proportion of 0.06:

z = (0.06 - 0.05) / 0.0146

= 0.0685

Using a standard normal distribution table or a calculator, we can find the probability associated with this z-score.

The probability is approximately 0.5307 (rounded to 4 decimal places).