Provide an appropriate response.
-The mean height for a population is 65 inches and the standard deviation is 3 inches. Let A and B
denote the events described below.
Event A: The mean height in a random sample of 16 people is within 1 inch of the population
mean.
Event B: The mean height in a random sample of 50 people is within 1 inch of the population mean.
The probability of event A is greater than the probability of event B?

Question

Quizplus · Accepted Answer

The probability of event B is greater than that of event A because, according to the Central Limit Theorem, as the sample size increases, the sampling distribution of the sample mean becomes more normally distributed and its standard deviation (standard error) decreases. This means that with a larger sample size (50 vs. 16), the sample mean is more likely to be closer to the population mean, making event B more probable.

Provide an Appropriate Response