Can you explain why these are the answers? Given two normal random variables: X~Normal(=6,=15) and Y~Normal(=15,=6).

What can be said about the points x=3 and y=15 when plotted in a STANDARD normal distribution? x and y both lie on the left side of the distribution

Answer: x is to the left of y Which follows from the Central Limit Theorem?

A. The sampling distribution of the sample mean is approximately normal even if the distribution of raw data values is not normal.

B. The sampling distribution of the sample mean is approximately normal if all possible samples are selected. Answer:

A

In a certain high school, it is believed that students having a weight of more than 125 lbs is considered overweight. Past data showed that the weights (in lbs) of high school students from this school is normally distributed with a standard deviation of 12.3 lbs. The principal of this high school would like to check if the current students are overweight. He took a random sample of 25 students and found out that the average weight is 107.6 lbs. The principal would like to estimate the true mean weight of the high school students in their school using a 90% confidence interval. If the principal wants to be 90% confident that the true mean weight of the high school students is within 3.5 lbs, what sample size is needed? Answer:

34