the time requiered for an aotumotive center to complete an oil change service on an automobile approximantely follows a normarl distribution, with a mean of 17 minutes and a standard deviation of 3 minutes. a) the automotive center guarantess customers that the service will take no longer than 20 minutes. if it does take longer, the customer will receive the service for half-price. what percent of customers receie the servefor half price? b) if the automotive center does not want to give the discount to more than 5% of its customers, how longt should it make the guaranteed time limit? a) the percent of customers that receive the service for half price is _______% (round to two decimal places as needed) b) the guarantedd time limit is _________ minutes (round to the nearest integer as needed)
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 time requiered for an aotumotive center to complete an oil change service on an automobile approximantely follows a normarl distribution, with a mean of 17 minutes and a standard deviation of 3 minutes.
a) the automotive center guarantess customers that the service will take no longer than 20 minutes. if it does take longer, the customer will receive the service for half-price. what percent of customers receie the servefor half price?
b) if the automotive center does not want to give the discount to more than 5% of its customers, how longt should it make the guaranteed time limit?
a) the percent of customers that receive the service for half price is _______% (round to two decimal places as needed)
b) the guarantedd time limit is _________ minutes (round to the nearest integer as needed)
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