Question

Based on historical data, your manager believes that 32% of the company's orders come from first-time customers. A random sample of 135 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is greater than than 0.33?

Answer 1

To find the probability that the sample proportion is greater than 0.33, you can use the normal distribution and the standard error formula.

Step-by-step explanation:

To find the probability that the sample proportion is greater than 0.33, we can use the normal distribution and the standard error formula. The standard error for estimating a proportion is given by:

SE = sqrt((p * (1 - p)) / n)

where p is the population proportion (0.32), and n is the sample size (135). Using this formula, we can calculate the standard error as:

SE = sqrt((0.32 * (1 - 0.32)) / 135) ≈ 0.0344

Next, we can calculate the z-score for a sample proportion of 0.33:

z = (0.33 - 0.32) / SE ≈ 0.029 / 0.0344 ≈ 0.8421

Finally, we can use the standard normal distribution table or a calculator to find the probability that the z-score is greater than 0.8421, which is approximately 0.1991 or 19.91%.

J11