Suppose the time it takes my daugther, Lizzie, to eat an apple is uniformly distributed between 5 and 12 minutes. Let X = the time, in minutes, it takes Lizzie to eat an apple. a. What is the distribution of X? X 2 Please show the following answers to 4 decimal places. b. What is the probability that it takes Lizzie at most 4 minutes to finish the next apple? c. What is the probability that it takes Lizzie less than 7.8 minutes to finish the next apple? d. What is the probability that it takes Lizzie between 6 minutes and 11.8 minutes to finish the next apple? e. What is the probability that it takes Lizzie fewer than 6 minutes or more than 11.8 minutes to finish the next apple?
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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