The Nielsen Media Group is a television rating company. On Monday, February 6, 2012, the day after the 2012 Super Bowl between the Giants and Patriots they reported that 40% of all US households had been tuned into the game the previous night. Suppose we take a random sample of 20 households the day after the game. Let X = # of households out of 20 that were tuned into the Super Bowl the previous night. 

a. What are the possible values of X?

b. Discuss why the Binomial model can be used to determine the probability distribution of X.

c. Assuming this rating is correct, what is the probability that in a random sample of 20 households, 2 or fewer would have been tuned into the game? 

d. What is the expected number of households in a random sample of 20 who would have been tuned into the game the previous night?

e. What is the standard deviation of the number of households in a random sample of 20 who would have been tuned into the game the previous night?