The lengths of your statistics class has a continuous uniform distribution between 46 minutes and 58 minutes. Let X be the length of a class in minutes. If one section is randomly selected, answer the following questions What is the distribution of X? What is the probability that the class is at most 55 minutes long? What is the probability that the class is less than 51 minutes or more than 56 minutes long?
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!
The lengths of your statistics class has a continuous uniform distribution between 46 minutes and 58 minutes. Let X be the length of a class in minutes. If one section is randomly selected, answer the following questions
What is the distribution of X?
- What is the
probability that the class is at most 55 minutes long? - What is the probability that the class is less than 51 minutes or more than 56 minutes long?
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