Lab 3 Answers

You can download and use the following file to answer the questions Lab 3 Answers File.docx Download Lab 3 Answers File.docx

1. Consider a binomial distribution with n=10 and p=0.1. (Remember that N=10 refers to the number of trials in a single binomial experiment where p is the probability of success in each trial.)  Using the terminology from class, how would you describe the shape of this binomial distribution?
2. Consider the same binomial distribution. Calculate the mean and the standard deviation of this binomial distribution using formulas from class.
3. Consider a sample of size n=35 from the same binomial distribution. (This means that you do the previously mentioned binomial experiment 35 times, the binomial experiment will still have 10 trials. So, this is ten trials done 35 times.)   What does the Central Limit Theorem tell you about the sampling distribution of $\overline{x}$?  Include the population mean and standard deviation of the sampling distribution, as well as a description of the shape of the distribution in your answer.
4. Copy and Paste the histogram you constructed into the uploaded document.
5. Calculate the mean and standard deviation of the 500 sample means.
6. Compare the shape of your histogram in 5 to your answer to problem 3, are they the same or different?  Did you expect this answer?  Why?
7. Compare the mean and standard deviation in problem 3 with the values you got from part D above.  Are they similar?  Should they be?
8. Overall, do your findings from problems 6 and 7 support your answer to problem 3? (Do they verify the Central Limit Theorem?)