Question: 9. A country has a standardized math test which is given to all their students at the end of their senior year at School. The

9. A country has a standardized math test which is given to all their students at the end of their senior year at School. The data from this test are approximately normal in shape with a mean # = 80 and a Standard Deviation of o = 6 (a) What are the probabilities of the following events. (i) A person chosen at random will have a Math Score of between 76 and 82? (ii) A person chosen at random will have a Math Score of less than 89? (iii) A person chosen at random will have a Math Score of greater than 100 (b) What score do you need to get to be at the 83"d percentile. (c) What score do you need to get to be in the top 5% of all students.3. A university conducts its own entrance exam - the mean of this exam is 1000 points with a standard deviation of 50. (a) A student gets a score of 960, what is the z-score for this student? (b) What percentage of students who take this entrance exam will get a score of 960 points or less? (c) In order to be eligible to join this university a student needs to score 1115 points or more. What percentage of students who take this entrance exam will be eligible to go to this university? (d) What score would you need to get in this entrance exam in order to be in the 95 percentile

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