8. A gas station has a 7% chance of running out of gas. [1] a) What is the probability the gas station will run out of gas one day in the next two weeks? [2] b) What is the probability the gas station will run out of gas at least two days in the next two weeks? [1] c) What is the expected number of times the gas station will run out of gas? 9. A co-ed soccer team has 9 women and 7 men on its roster. 6 players play on the field at one time. [2] a) What is the probability the starting lineup will have 3 men and 3 women on it? [3] b) What is the probability the starting lineup will have at least 5 men on it? [2] c) What is the expected number of women on the team? 10. speed trap on the highway set by the O.P.P. shows that the mean speed of cars is 103.4 km/h with a standard deviation of 9.8 km/h. The posted speed limit on the highway is 100 km/h. [2] a) What percentage of drivers are technically driving under the speed limit? [2] b) Speeders caught traveling 25 km/h or more over the speed limit are subject to a $5000 fine. What percentage of speeders will be fined $5000? [2] c) Police officers tend not to pull over drivers between 100 km/h and 110 km/h. What percentage of drivers is this? [2] d) The top 2% of all drivers speeding are subject to losing their license. According to the data, what speed must a driver be traveling to lose his or her license? 11. A lacrosse team has been in its premier league for the last 47 seasons. During this time they have a mean number of wins of 17.3 and a standard deviation of 2.2 wins. [2] a) What is the probability of the lacrosse team getting 21 wins in the upcoming season? [3] b) What is the probability of the lacrosse team getting between 15 and 18 wins? 12. A cruise ship has a 74% chance of having leftover rooms the week before the cruise. There are 25 cruise ships setting sail this month. [1] a) Is it possible to approximate this binomial distribution using a normal approximation? [2] b) What is the mean and the standard deviation for this approximation? [2] c) What is the probability that exactly 20 cruise ships will have leftover rooms using the normal approximation? [2] d) How different is the normal approximation from the binomial distribution value? Calculate the probability that exactly 20 cruise ships will have leftover rooms using the binomial method