A study found that the mean amount of time cars spent in drive-throughs of a certain fast-food restaurant was 147.1 seconds. Assuming drive-through times are normally distributed with a standard deviation of 34 seconds, complete parts (a) through (d) below. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) What is the probability that a randomly selected car will get through the restaurant's drive-through in less than 95 seconds? The probability that a randomly selected car will get through the restaurant's drive-through in less than 95 seconds is 0.0630. (Round to four decimal places as needed.) (b) What is the probability that a randomly selected car will spend more than 205 seconds in the restaurant's drive-through? The probability that a randomly selected car will spend more than 205 seconds in the restaurant's drive-through is- (Round to four decimal places as needed.)

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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!