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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 the expected value μ = 57.9% and the standard deviation o = 14.0%, ic X~ N(57.9; 14.0). (a) Find the probability that a randomly selected student has more than 60% correctly 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% correctly on the math exam? 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%? A sample of 9 students had the following result (measured in percent) on the exam in mathematics: 41.3 63.7 35.7 87.1 37.9 53.5 58.6 49.5 25.4 (d) Find a 99% confidence interval for expected value mu for results based on these mea- surements. We now assume that the standard deviation sigma is unknown and that the results are independent of each other. (e) Based on the sample of 9 students, is there any reason to claim that the expected value u for the result of the examination in mathematics has changed? Formulate the hypotheses Ho and H₁. Test the hypotheses at significance level = 0.01 and conclude whether the hypothesis Ho should be rejected or retained.

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 the expected value μ = 57.9% and the standard deviation o = 14.0%, ic X~ N(57.9; 14.0). (a) Find the probability that a randomly selected student has more than 60% correctly 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% correctly on the math exam? 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%? A sample of 9 students had the following result (measured in percent) on the exam in mathematics: 41.3 63.7 35.7 87.1 37.9 53.5 58.6 49.5 25.4 (d) Find a 99% confidence interval for expected value mu for results based on these mea- surements. We now assume that the standard deviation sigma is unknown and that the results are independent of each other. (e) Based on the sample of 9 students, is there any reason to claim that the expected value u for the result of the examination in mathematics has changed? Formulate the hypotheses Ho and H₁. Test the hypotheses at significance level = 0.01 and conclude whether the hypothesis Ho should be rejected or retained.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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 the expected value μ = 57.9% and the standard deviation o = = 14.0%, ic X~ N(57.9; 14.0). (a) Find the probability that a randomly selected student has more than 60% correctly 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% correctly on the math exam? 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%? A sample of 9 students had the following result (measured in percent) on the exam in mathematics: 41.3 63.7 35.7 87.1 37.9 53.5 58.6 49.5 25.4 (d) Find a 99% confidence interval for expected value mu for results based on these mea- surements. We now assume that the standard deviation sigma is unknown and that the results are independent of each other. (e) Based on the sample of 9 students, is there any reason to claim that the expected value for the result of the examination in mathematics has changed? Formulate the hypotheses Ho and H₁. Test the hypotheses at significance level a = 0.01 and conclude whether the hypothesis Ho should be rejected or retained.
Transcribed Image Text: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 the expected value μ = 57.9% and the standard deviation o = = 14.0%, ic X~ N(57.9; 14.0). (a) Find the probability that a randomly selected student has more than 60% correctly 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% correctly on the math exam? 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%? A sample of 9 students had the following result (measured in percent) on the exam in mathematics: 41.3 63.7 35.7 87.1 37.9 53.5 58.6 49.5 25.4 (d) Find a 99% confidence interval for expected value mu for results based on these mea- surements. We now assume that the standard deviation sigma is unknown and that the results are independent of each other. (e) Based on the sample of 9 students, is there any reason to claim that the expected value for the result of the examination in mathematics has changed? Formulate the hypotheses Ho and H₁. Test the hypotheses at significance level a = 0.01 and conclude whether the hypothesis Ho should be rejected or retained.
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