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 within 3 inches of the population mean.
Event B: The mean height in a random sample of 16 people is within 3 inches of the population
mean.
The probability of event A is greater than the probability of event B?

Question

Quizplus · Accepted Answer

Event A refers to the probability of a single measurement falling within a certain range, while Event B concerns the probability of the mean of a sample of measurements falling within that range. Due to the Central Limit Theorem, the distribution of sample means (Event B) will be more tightly clustered around the population mean than individual measurements (Event A), making the probability of Event B being within 3 inches of the population mean higher than that of Event A.

Provide an Appropriate Response