A lawyer commutes daily from his suburban home to his office. The average time for a one-way trip is 30 minutes with a standard deviation of 4.2 minutes. Assume the distribution of duration of commute to be normal, (a) what is the probability that the trip will take at least ½ hour? (b) If the office opens at 9:00 am and he leaves his house at 8:45 am daily, what percentage of the time is he late for work? (c) Find the length of time above which we find the slowest 15% of the trips. (d) Find the probability that 2 of the next 3 trips will take at least ½ hour.
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!
A lawyer commutes daily from his suburban home to his office. The average time for a one-way trip is 30 minutes with a standard deviation of 4.2 minutes. Assume the distribution of duration of commute to be normal, (a) what is the
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