In the game of roulette, a player can place a $7 bet on the number 11 and have a 138

probability of winning. If the metal ball lands on 11, the player gets to keep the $7 paid to play the game and the player is awarded an additional $245. Otherwise, the player is awarded nothing and the casino takes the player's $7.

What is the expected value of the game to the player? If you played the game 1000 times, how much would you expect to lose?

According to a study done by Nick Wilson of Otago University Wellington, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and observe people's habits as they sneeze. Complete parts (a) through (c).

(a) What is the probability that among

12

randomly observed individuals, exactly

4

do not cover their mouth when sneezing?Using the binomial distribution, the probability is

enter your response here.

(Round to four decimal places as needed.)Part 2(b) What is the probability that among

12

randomly observed individuals, fewer than

3

do not cover their mouth when sneezing?Using the binomial distribution, the probability is

enter your response here.

(Round to four decimal places as needed.)Part 3(c) Would you be surprised if, after observing

12

individuals, fewer than half covered their mouth when sneezing? Why?

No,

Yes, it would not would be surprising, because using the binomial distribution, the probability is

enter your response here, which is

greater than

less than 0.05.(Round to four decimal places as needed.)