A professor gives two types of quizzes, objective and recall. He is planning to give at least 15 quizzes this quarter. The student preparation time for an objective quiz is 15 minutes and for a recall quiz 30 minutes. The professor expects a student to spend at least 5 hours (300 minutes) preparing for these quizzes. The average score on an objective quiz is 7 points, and on a recall quiz is 5 points, and the professor would like the average student to score at least 85 points on all quizzes. It takes the professor 1 minute to grade an objective quiz, and 1.5 minutes to grade a recall type quiz. How many of each type of quiz should he give in order to minimize his grading time?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
A professor gives two types of quizzes, objective and recall. He is planning to give at
least 15 quizzes this quarter. The student preparation time for an objective quiz is 15
minutes and for a recall quiz 30 minutes. The professor expects a student to spend at least
5 hours (300 minutes) preparing for these quizzes. The average score on an objective quiz
is 7 points, and on a recall quiz is 5 points, and the professor would like the average
student to score at least 85 points on all quizzes. It takes the professor 1 minute to grade
an objective quiz, and 1.5 minutes to grade a recall type quiz. How many of each type of
quiz should he give in order to minimize his grading time?
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