The following table is based on information taken from Trends in the U.S. for shoppers who purchased at least 70% of their items on sale. Round answers to the nearest hundredth. A. Using the age midpoints x and the percentage of shoppers, is this a valid probability distribution? Explain. B. Compute the expected age of a shopper. C. Compute the standard deviation for the ages of the shoppers.
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 following table is based on information taken from Trends in the U.S. for shoppers
who purchased at least 70% of their items on sale. Round answers to the nearest hundredth.
A. Using the age midpoints x and the percentage of shoppers, is this a valid
B. Compute the expected age of a shopper.
C. Compute the standard deviation for the ages of the shoppers.
Solution:
| Age Years | Midpoint (x) | percent of shoppers P(X) | |||
| 18-28 | 23 | 0.14 | 3.22 | 529 | 74.06 |
| 29-39 | 34 | 0.24 | 8.16 | 1156 | 277.44 |
| 40-50 | 45 | 0.44 | 19.8 | 2025 | 891 |
| 51-61 | 56 | 0.07 | 3.92 | 3136 | 219.52 |
| 62 and over | 67 | 0.11 | 7.37 | 4489 | 493.79 |
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