The descriptive statistics for the variable (Coin) where each of the thirty-five students flipped a coin 10 times. Round your answers to three decimal places and type the mean and the standard deviation in the grey area below.

Mean: 4.4

Standard Deviation: 1.499

1. Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being ½ and n = 10. Either show work or explain how your answer was calculated. Use these formulas to do the hand calculations: Mean = np, Standard Deviation =

Mean = np:

Standard Deviation = :

2. Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being ¼ and n = 10. Write a comparison of these statistics to those from question 5 in a short paragraph of several complete sentences. Use these formulas to do the hand calculations: Mean = np, Standard Deviation =

Mean = np:

Standard Deviation = :

Comparison:

3. Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being ¾ and n = 10. Write a comparison of these statistics to those from question 6 in a short paragraph of several complete sentences. Use these formulas to do the hand calculations: Mean = np, Standard Deviation =

Mean = np:

Standard Deviation = :

Comparison:

4. Using all four of the properties of a Binomial experiment (see page 201 in the textbook) explain in a short paragraph of several complete sentences why the Coin variable from the class survey represents a binomial distribution from a binomial experiment.