Use Excel to illustrate the Central Limit Theorem when sampling from a binomial

Question

Use Excel to illustrate the Central Limit Theorem when sampling from a binomial distribution.

a). Generate at least 1000 random samples (you can generate more if you wish), each with 4 observations, from a binomial random variable y where p=0.2 (the probability of a success), and n=10 trials. That is, the random variable y represents the number of successes in 10 trials, where the probability of a success is 0.2. Calculate the sample mean for each sample.
- Plot a frequency histogram of the sample means and comment on the plot. Determine the range, mean and standard deviation of the 1000 sample means. How do the calculated mean and standard deviation compare with what you would expected from a theoretical analysis?

b). Generate at least 1000 random samples (you can generate more if you wish), each with 30 observations, from a binomial random variable y where p=0.2 (the probability of a success), and n=10 trials. That is, the random variable y represents the number of successes in 10 trials, where the probability of a success is 0.2. Calculate the sample mean for each sample.
-Plot a frequency histogram of the sample means and comment on the plot. Determine the range, mean and standard deviation of the 1000 sample means. How do the calculated mean and standard deviation compare with what you would have expected from a theoretical analysis? Request: Could you please include the excel files in this solution? Thanks! Use Excel to illustrate the Central Limit Theorem when sampling from a binomial distribution.

a). Generate at least 1000 random samples (you can generate more if you wish), each with 4 observations, from a binomial random variable y where p=0.2 (the probability of a success), and n=10 trials. That is, the random variable y represents the number of successes in 10 trials, where the probability of a success is 0.2. Calculate the sample mean for each sample.
- Plot a frequency histogram of the sample means and comment on the plot. Determine the range, mean and standard deviation of the 1000 sample means. How do the calculated mean and standard deviation compare with what you would expected from a theoretical analysis?

b). Generate at least 1000 random samples (you can generate more if you wish), each with 30 observations, from a binomial random variable y where p=0.2 (the probability of a success), and n=10 trials. That is, the random variable y represents the number of successes in 10 trials, where the probability of a success is 0.2. Calculate the sample mean for each sample.
-Plot a frequency histogram of the sample means and comment on the plot. Determine the range, mean and standard deviation of the 1000 sample means. How do the calculated mean and standard deviation compare with what you would have expected from a theoretical analysis? Request: Could you please include the excel files in this solution? Thanks!

Explanation / Answer

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