PROBLEM 1: Final grades in Professor Booba's course are calculated as a weighted average of the midterm and final exam. The midterm is weighted at 0.4 and the final is weighted at 0.6. Semester grades on the midterm exam were normally distributed with $\mu_m = 63$ and $\sigma^2_m = 14$. Grades on the final exam were also normally distributed with $\mu_f = 75$ and $\sigma^2_f = 20$. Performance on both exams were positively correlated with a sample covariance, $\sigma_{mf} = 0.05$, Question 1 Refer to Problem 1. The average final grade in Professor Booba's course is Blank 1 (Please enter two decimals) Blank 1 Add your answer Question 2 Refer to Problem 1. The variance of the distribution of final grades was Blank 1 (please enter two decimals) Blank 1 Add your answer
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4·M + 0.6·F. The mean is E[G] = 0.4·μ_m + 0.6·μ_f = 0.4·63 + 0.6·75 = 25.20 + 45.00 = 70.20. Show more…
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A professor wants to know if her introductory statistics class has a good grasp of basic math. Six students are chosen at random from the class and given a math proficiency test. The professor wants the class to be able to score above 70 on the test. The six students get scores of 62, 92, 75, 68, 83, and 95. Questions: 1. What statistical test do you suggest to answer the problem? 2. Set the null and alternative hypotheses. 3. Compute the sample mean and the standard deviation. 4. Can the professor have 90 percent confidence that the mean score for the class on the test would be above 70?
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