Question

Suppose you want to use a confidence interval to estimate the true mean number of calories found in candy bars. It is known that the distribution of the calories is normal. How many candy bars must you have in order to be sure the sampling distribution of x is normal?

Answer 1

See explanation

Explanation:

Solution:-

- To estimate the true mean number of calories found in candy bars we need a confidence interval for the distribution.

- Assuming population is normally distributed. We take a sample of "n" number of candies from the population. It is given that the sample conforms to the condition of normality irrespective of the sample size "n"

- If the population is not normally distributed then to approximate the sample for normality then the sample size must be large enough for it to be covered throughout 3 standard deviations.

- It is found through empirical results that "sufficient large" sample size of n:

n ≥ 30

- Complies with the conditions of normality.

Answer 2

See explaination.

Explanation:

Sampling distribution can be defined as a probability distribution of a statistic which is gotten through a large number of samples usually drawn from a specific population.

The sampling distribution of a given population can be described as the distribution of frequencies of a range of different outcomes that could possibly occur for a statistic of a population.

Please refer to attachment for a step by step technique to prove How many candy bars must you have in order to be sure the sampling distribution of x is normal.