The time X(mins) for Ayesha to prepare breakfast for her family is believed to have a uniform distribution with A=25 and B=35. a) Determine the pdf of X and draw its density curve. b) What is the probability that time taken by Ayesha to prepare breakfast exceeds 33 mins? c) What is the probability that cooking or preparation time is within 2 mins of the mean time? (Hint: Identify mean from the graph of f(x))
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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