The stochastic variable X is the proportion of correct answers (measured in percent) on the exam in mathematics for a random engineering student. We assume that X is normally distributed with expectation value µ = 57, 9% and standard deviation σ = 14, 0%, ie X ∼ N (57, 9; 14, 0). (a) Find the probability that a randomly selected student has more than 60% correct on the exam in mathematics, ie P (X> 60). (b) Consider 81 students from the same cohort. What is the probability that at least 30 of them get over 60% correct on the exam in mathematics? We assume that the students results are independent of each other. (c) Consider 81 students from the same cohort. Let X¯ be the average value of the result (measured in percent) on the exam in mathematics for 81 students. What is the probability that X¯ is above 60%?
The stochastic variable X is the proportion of correct answers (measured in percent) on the exam in mathematics for a random engineering student. We assume that X is
(a) Find the probability that a randomly selected student has more than 60% correct on the exam in mathematics, ie P (X> 60).
(b) Consider 81 students from the same cohort. What is the probability that at least
30 of them get over 60% correct on the exam in mathematics? We assume that the students
results are independent of each other.
(c) Consider 81 students from the same cohort. Let X¯ be the average value of the result (measured in percent) on the exam in mathematics for 81 students. What is the probability that X¯ is above 60%?
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