Show All Work!!! The company Uniyic has 8 members on its board of directors. In how many different ways can it elect a president. vice-president, secretary and treasurer? (7 points) A three-person committee is to be elected from an organization's membership of 10 people. How many different committees are possible? (7 points) In a race in which ve automobiles are entered and there are not ties, in how many ways can the rst four nishers come in? (7 points) The model of the car you are thinking of buying is available in six different colors and two different styles (hatchback or sedan). In how many ways can you order the car? (7 points) A book club offers a choice of 7 books from a list of 30. In how many ways can a member make a collection? (7 points) . Determine if the following are probability distributions (if no. state why). (10 points) a. X 3 6 9 12 15 P(X) 419 2:9 2:9 1:9 0 b.X l 2 3 4 5 P(X)3f10 1:10 1:10 2:10 4;\"10 Construct a probability distribution for the data: (Hint: Round the probabilities to the nearest hundredth) (8 points) A box contains 4 $1 bills, 2 $5 bi]ls_._ 2 $10 bill. and 1 $20 bill. X P(X) Below is a probability distribution for the number of math failures of BC students. Complete the blank considering you have a probability distribution. (12 points) X 0 1 2 3 4 P(X) 0.31 0.28 0.08 0.02 P(X = 2) = . What is the probability to have no more than two math failures? What is the probability to have at least two inath failures? . What is the probability to have at most one math failures? 9. The number of suits sold per day at Suit World is shown in the probability distribution below. (10 points) X 2 4 5 9 P(X) 0.3 0.3 0.2 0.2 Find the mean. variance. and standard deviation of the distribution. X P(X) Mean = Variance = Standard Deviation = 10. A medical treatment is successful 76% of the time. A hospital wishes to treat a group of patients. How many patients should they take so that the probability that all are cured is 0.05? (5 points) 11. A manufacturer makes 10 000 ball point pens per dayr and estimates that 150 will be defective. She decides that if a random sample of 20 pens contains more than one defective pen, then she will institute quality-control measures. (5 points) a) Find the probability that there are more than one defective. 12. A drug company claims their new u vaccine cures 89% of patients. What is the probability that in a family of five people who take the vaccine? (a) At most four get the u? (5 points) (b) At least one gets the u? (5 points) 13. Ime- Bi (10, 0.4), nd (5 points) (a) PCX: 9) (Extra Credit 5 points) (b) P (X: 1)