HELP PLEASE! I am on edmentum and this question has multiple answers! Select all the correct answers.
Which statements regarding the implications of the central limit theorem are true?

1. For an infinite number of samples, 95% of the sample means would fall within the interval .
2. The mean of the population is the same as the mean of any sample taken from the population.
3. If the population is normally distributed, then the mean of a sample from that population will be normally distributed.
4. As the number of sample means decreases, the means get closer to a standard normal distribution.
5. The central limit theorem holds true only for populations that are normally distributed.
6. For an infinite number of samples, 99.7% of the sample means would fall within the interval .

Abottled water distributor wants to estimate the amount of water contained in 1-gallon bottles purchased from a nationally known water bottling company. the water bottling company’s specifications state that the standard deviation of the amount of water is equal to 0.02 gallon. a random sample of 50 bottles is selected, and the sample mean amount of water per 1-gallon bottle is 0.995 gallon a. construct a 99% confidence interval estimate for the popula-tion mean amount of water included in a 1-gallon bottle. b. on the basis of these results, do you think that the distributor has a right to complain to the water bottling company? why? c. must you assume that the population amount of water per bottle is normally distributed here? explain. d. construct a 95% confidence interval estimate. how does this change your answer to (b)?