Med 140 #2 - Page 5 of 6 money you are expected to earn by the end of the game) Take the money 7. Based on a Harris Interactive poll, 80% of adults believe that Mcdonald's french fries taste the best. Assume that seven adults are randonly selected, and find the indicated probabilities. (a) (5 points) What is the probability that exactly five of the selected adults believe Mcdon- ald's french fries taste the best? . 275 (b) (5 points) What is the probability that all of the selected adults believe that Mcdonald's french fries taste the best? of 0 4. 004 +. 029 1. 115 + - 275 +. 767 Probability = 0. 79 - 2 .5 (c) (5 points) What is the probability that at least 2 adults believe Mcdonald's french fries taste the best? - 2 .5 (d) (5 points) If seven adults are randomly selected, is six adults an unusually high number who believe that Mcdonald's french fries taste the best? it is not Why ??Tage G ur S 8. In astudy of 420.095 cell phone users in America, it was found that 135 developed cancer of the brain or nervour system. If we assume that the use of cell phones has no effect on developing such a cancer, then the probability of a person have such a cancer is 0.000340. (Assume a Binimial Distribution) (a) (7 points) Assuming that cell phones have no effect on developing cancer, find the mean and standard deviation for the numbers of peoplle in groups of 420,095 that can be expected to have cancer of the brain or nervous system. P/v ) ( n - x ) ! x ! ' ( P ) * . ( 9 ) ' n - X P = 0. 010310 n: 135 9- 1 - 0.02 742 = 0. 999 MEinp - 3.5 = ( 135 ) (0. 00 0 3 40 ) (1) = 0. 046 05 0. 459 - 0. 68 (b) (3 points) Based on the result from the previous question, is 135 cases of cancer of the brain or nervous system a unusually low or high number? M - 20 M MID M 120 - 1. 514 -634 0-046 0- 726 1.40 6 135 is unusually high number(c) (2 points) If it is a probability distribution draw a smiley face. If it is not explain how it failed. 5. (10 points) In a certain country, the true probability of a baby being a girl is 0.463. Among the next nine randomly selected births in the country, what is the probability that at least one of them is a boy? Show your work and round your answer to three decimal places. Let g = baby is a girl, then P(g) = 0.463. Let b = baby is a boy. P(at least one b) = P ( . ) - 0. 463 = 0. 463 X - 4 0. 0 05 6. You're on a game show and given the option of taking $800 cash or playing a dice game with the following rules. You will roll the dice 10 times. Each 1 that you roll you win $300, each 2 or 3 that you roll you win $150, each 4 or 5 you roll you win $120 and every 6 you roll you lose $450 of your winnings. (a) (8 points) Calculate the expected value for the dice game for any single roll Ive Roll" 1 1-11 ($320 ) ## 300 2 2 or 3 ( 152 ) = 1700 3 4 5 ( 120 ) - 1240 4 4 x (- 450 ) = - 450 1 - 450 C J (b) (2 points) Should you play the game or take the money based on the expected value? (hint: Multiply the single roll expected value by 10 to determine how much Take the money4. Determine if the following table represents a probability distribution. X p(x 0 0.125 1 0.250 Yes, it does representa 2 0.400 3 0.100 probability Distribution 4 0.025 (a) (6 points) What are the three requirements for this to be a probability distribution? 1) x represents in numerical form 2 ) 8 P ( x ) = 1 all sums must be I or O. 999 or/ ool 3 ) 0