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 height of a randomly selected person is 5 inches or more from the population mean.
Event B: The mean height in a random sample of 16 people is 5 inches or more from the population
mean.
The probability of event A is greater than the probability of event B?

Question

Quizplus · Accepted Answer

Event A involves the height of a single individual deviating from the mean by 5 inches or more, which is relatively more likely given the standard deviation of 3 inches. Event B involves the mean height of a sample of 16 people deviating by 5 inches or more from the population mean, which is less likely due to the Central Limit Theorem, as the standard deviation of the sample mean (standard error) is smaller than the population standard deviation.

Provide an Appropriate Response