Between 12:00 pm and 1:00 pm, cars arrive at Citibank’s drive-thru at the rate of 6 cars per hour (0.1 car per minute). The following formula fromprobability can be used to determine the probability that a car will arrive within t minutes of 12:00 pm.F(t) = 1 - e-0.1t (a) Determine the probability that a car will arrive within 10 minutes of 12:00 pm (that is, before 12:10 pm).(b) Determine the probability that a car will arrive within 40 minutes of 12:00 pm (before 12:40 pm).(c) What value does F approach as t becomes unbounded in the positive direction?(d) Graph F using a graphing utility.(e) Using INTERSECT, determine how many minutes are needed for the probability to reach 50%.
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!
Between 12:00 pm and 1:00 pm, cars arrive at Citibank’s drive-thru at the rate of 6 cars per hour (0.1 car per minute). The following formula from
probability can be used to determine the probability that a car will arrive within t minutes of 12:00 pm.
F(t) = 1 - e-0.1t
(a) Determine the probability that a car will arrive within 10 minutes of 12:00 pm (that is, before 12:10 pm).
(b) Determine the probability that a car will arrive within 40 minutes of 12:00 pm (before 12:40 pm).
(c) What value does F approach as t becomes unbounded in the positive direction?
(d) Graph F using a graphing utility.
(e) Using INTERSECT, determine how many minutes are needed for the probability to reach 50%.
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