The time required to prepare a certain specialty coffee at a local coffee shop is uniformly distributed between 30 and 50 seconds. Assuming a customer just ordered one of these specialty coffees, determine the probabilities described below. a. What is the probability that the preparation time will be more than 33 seconds? b. What is the probability that the preparation time will be between 39 and 46 seconds? c. What percentage of these specialty coffees will be prepared within 43 seconds? d. What is the standard deviation of preparation times for this specialty coffee at this shop?
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!
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