Green M&M?s: Consider a class of 20 statistics students, where each student is given 5 small bags of M&M?s and asked to count the number of green M&M?s. The results are shown below. The population mean is for a bag of this size is 10.06 and the population standard deviation is 2.59.

Answer the following questions:

a. Find the sample means for each student?s green M&M count.

b. Create a histogram of the sample means, and calculate the mean and standard deviation of the sample means. To construct a histogram, follow the given steps:

I.Obtain a frequency (relative-frequency, percent) distribution of the data.

II.Draw a horizontal axis on which to place the bars and a vertical axis on which to display the frequencies (relative frequencies, percents).

III.For each class, construct a vertical bar whose height equals the frequency (relative frequency, percent) of that class.

IV.Label the bars with the classes, the horizontal axis with the name of the variable, and the vertical axis with ?Frequency? (?Relative frequency,? ?Percent?).

c. Theoretically, what are the mean, standard deviation, and distribution of all possible sample means for a sample size of 5?

Bag1 Bag 2 Bag 3 Bag 4 Bag 5 4 7 6 14 14 18 8 18 8 13 12 7 11 18 9 14 10 12 Student 1 3 Student 2 12 Student 3 12 Student 4 18 Student 5 17 Student 6 3 Student 7 3 Student 86 Student 9 8 Student 10 14 Student 11 3 Student 12 7 Student 13 17 Student 14 9 Student 15 14 Student 16 4 Student 17 11 Student 18 15 Student 19 4 Student 20 12 2 16 13 14 14 8 9 14 11 2 18 8 16 3 17 12 3 12 11 17 11 12 7 6 17 13 5 11 9 9 18 17 3 17 5 17 15 7 2 18 13 11 10 3 12 14 13 10 16 16 5 3 11 16 14 11 8 2 13 15 11