9. From a pool of fifteen candidates the offices of president,vice-president and

Question

9. From a pool of fifteen candidates the offices of president,vice-president and secretary will be filled. In how many ways canthe offices be filled if each candidate can hold any office?

10. When two cards are drawn from a well-shuffled deck of 52playing cards, what are the probabilities of getting:

a. two aces b. two face cards c. two black cards

13. Public school students taking a mathematics assessment had amean score of 290 with a standard deviation of 37. Possible testscores could range from 0 to 500. Assume that the test scores arenormally distributed:

a. What percentage of the students had a score between 250 and 300?__________
b. What is the lowest score that would still place a student in thetop 5% of the scores? ___________

14. Assuming a normal distribution, in order to be graded extralarge, an egg must weigh at least 2.2 oz. If the average weight foran egg is 1.5 oz., with a standard deviation of 0.4 oz., how manyof twenty dozen eggs would you expect to grade extra large?____________

Explanation / Answer

9) After 1 of the 15 candidates is selected for president, thereare 14 left to fulfill the office of the VP, and then there are 13left for the spot of the secretary. Thre is a total of 15 x 14 x 13= 2730 ways. 10) a) (2/52) * (1/51) = 0.000754 since there is no replacement b) There are a total of 3 x 4 = 12 face cards in the deck. (12/52)* (11/51) = 0.04977 c) There are a total of 52/2 = 26 black cards in the deck. (26/52)* (25/51) = 0.2451 13. a) P(250 1.645) = 0.95 1.645 = (x - 290)/37 x = 350.86 ˜ 351 14. P(X > 2.2) = 1 - P(X < 2.2) = 1 - P(Z < (2.2-1.5)/0.4)= 1 - P(Z < 1.75) = 0.04 20 x 0.04 = 0.8 ˜ 1

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