he probability density function of the time a customer arrives at a terminal (in minutes after 8:00 A.M.) is f(x) = 0.25 e-x/4 for x > 0. Determine the probability that (a) The customer arrives by 10:00 A.M. (Round your answer to one decimal place (e.g. 98.7)) (b) The customer arrives between 8:19 A.M. and 8:31 A.M. (Round your answer to four decimal places (e.g. 98.7654)) (c) Determine the time (in hours A.M. as decimal) at which the probability of an earlier arrival is 0.51. (Round your answer to two decimal places (e.g. 98.76))
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!
The
(a) The customer arrives by 10:00 A.M. (Round your answer to one decimal place (e.g. 98.7))
(b) The customer arrives between 8:19 A.M. and 8:31 A.M. (Round your answer to four decimal places (e.g. 98.7654))
(c) Determine the time (in hours A.M. as decimal) at which the probability of an earlier arrival is 0.51. (Round your answer to two decimal places (e.g. 98.76))
(d) Determine the cumulative distribution function and use the cumulative distribution function to determine the probability that the customer arrives between 8:19 A.M. and 8:31 A.M. (Round your answer to four decimal places (e.g. 98.7654))
(e) Determine the mean and
(f) standard deviation of the number of minutes until the customer arrives. (Round your answers to one decimal place (e.g. 98.7))
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