Question 17 0 / 1 point If a data set has a normal distribution, what percentage of the data falls between x" and x120? O 0.68 O 0.34 .g. Q 0.95 O 0.475 Question 18 0 / 1 point A box contains 12 green marbles and 8 red marbles. Two are chosen randomly, one at a time, without replacement. Determine the probability that you draw a green marble followed by a red marble. O 0.253 O 0.505 O 0.5 0 0.0026 q. 0 0.253 Question 19 0 / 1 point Two events are mutually exclusive and independent. If P(A) = 0.54 and P(B) = 0.2, what is the probability of getting A or B? O 0.108 O 0.54 .g. Q 0.74 O 0.2 10. You are almost done your Data Management exam, and your teacher hands you the multiple choice section. There are 24 questions, with four possible answers for each. You have under a minute to answer them, so you start guessing. Later, you try to estimate the chances of getting a good mark. a) Can the normal approximation to the binomial distribution be used? Justify your answer and describe why it is important to check that the normal approximation can be used. (4 marks) b) Calculate the probability that you get at least 8 of the 24 questions correct, using the normal approximation to the binomial distribution. (5 marks) 11. The weights of the students at a local high school are normally distributed with a mean of 68 kg and a standard deviation of 4 kg. at) Determine the percentage of students who weigh more than 73 kg. (3 marks) b) Determine the percentage of students who weight between 54 kg and 70 kg. (4 marks) a z=(73-68)/4=5/4=1.25 Therefore, 0.5 0.3944 = 0.1056 = 10.56%-Please explain. Thank you. b) z=(70-68)/4=2/4=0.5 z=(68-54)/4=14/4=3.5 Therefore, 0.1915 + 0.4998 = 0.6913 = 69.13%-Please explain. Thank you. 12. A geologist mixes 10 rocks with fossils into a bag with 90 other similarly sized rocks that do not contain fossils. She then removes 20 rocks from the bag at random. What is the probability she will get exactly 3 fossils? (2 marks) What is the probability she will get less than 3 fossils? (3 marks) What is the probability she will get at least 4 fossils? (3 marks). (Hint: Use the indirect method)