Mr. Patel normally walks from his home at Meadows to his office at ACH and back to home everyday through the same road. Assume that his total commute time is uniformly distributed between 16 minutes and 24 minutes. Also assume that he walks at the same speed every time. a. What is the probability that on any given day, he takes less than 10 minutes to reach his office from his home? b. What is the expected time for reaching office from his home? c. What is the variance in time for his total commute 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!
Mr. Patel normally walks from his home at Meadows to his office at ACH and back to home everyday through the same road. Assume that his total commute time is uniformly distributed between 16 minutes and 24 minutes. Also assume that he walks at the same speed every time.
a. What is the probability that on any given day, he takes less than 10 minutes to reach his office from his home?
b. What is the expected time for reaching office from his home?
c. What is the variance in time for his total commute time
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