Question

A researcher reports survey results by stating that the standard error of the mean is 20. The population standard deviation is 440.

a. What is the probability that the point estimate was within ±30 of the population mean? (Round your answer to four decimal places.)

Answer 1

The probability that the point estimate is within ±30 of the population mean is 50%.

Step-by-step explanation:

To find the probability that the point estimate is within ±30 of the population mean, we need to calculate the z-score for ±30 using the standard error of the mean. The z-score formula is (point estimate - population mean) / standard error of the mean. In this case, the point estimate is 0 because we want to find the probability of being within ±30 of the population mean. So the z-score is (0 - 0) / 20 = 0. To find the probability, we look up the z-score in the standard normal distribution table. The cumulative probability for a z-score of 0 is 0.50. However, we want the probability of being within ±30, so we subtract 0.50 from 1 to get 0.50. Therefore, the probability that the point estimate is within ±30 of the population mean is 0.50 or 50%.