Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found to be normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes. i. What is the probability that a randomly selected individual will have a waiting time of at least 10 minutes? ii. What is the probability that a randomly selected individual will have a waiting time between 15 and 45 minutes? iii. Suppose that in an effort to provide better service to the public, the director of the local office is permitted to provide discounts to those individuals whose waiting time exceeds a predetermined time. The director decides that 15 percent of the customers should receive this discount. What number of minutes do they need to wait to receive the discount?
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!
Suppose that the waiting time for a license plate renewal at a local office of a state
motor vehicle department has been found to be
30 minutes and a standard deviation of 8 minutes.
i. What is the probability that a randomly selected individual will have a waiting
time of at least 10 minutes?
ii. What is the probability that a randomly selected individual will have a waiting
time between 15 and 45 minutes?
iii. Suppose that in an effort to provide better service to the public, the director of
the local office is permitted to provide discounts to those individuals whose
waiting time exceeds a predetermined time. The director decides that 15
percent of the customers should receive this discount. What number of
minutes do they need to wait to receive the discount?
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