A) The amount of time it takes students to complete a Statistics II quiz is uniformly distributed between 30 to 60 minutes. One student is selected at random. Find the following: a. The probability density function (pdf) of amount of time taken for the quiz. b. The probability that the student requires more than 50 minutes to complete the quiz. c. The probability that the student completes the quiz in a time between 35 and 40 minutes. d. The probability that the student requires at least 45 minutes to complete the quiz. e. The probability that the student completes the quiz exactly 52 minutes. f. Compute the expected time and the coefficient of variation to complete the quiz.
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!
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