Number of Bagels Sold in One Day Probability .05 .10 10 .10 15 .20 20 .25 25 .15 30 .10 35 .05
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!
Billy’s Bakery bakes fresh bagels each morning. The daily demand for bagels is a random variable with a distribution estimated from prior experience given by
The bagels cost Billy’s 8 cents to make, and they are sold for 35 cents each.
Bagels unsold at the end of the day are purchased by a nearby charity soup kitchen for 3 cents each.
a. Based on the given discrete distribution, how many bagels should Billy’s bake at the start of each day? (Your answer should be a multiple of 5.)
b. If you were to approximate the discrete distribution with a
c. Determine the optimal number of bagels to bake each day using a normal approximation. (Hint: You must compute the mean μ and the variance σ2 of the demand from the given discrete distribution.)
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