he management of a supermarket wants to adopt a new promotional policy of giving free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditure for all customers at this supermarket will be normally distributed with mean 400 L.E and a variance of 900 L.E2. 1) If the management wants to give free gifts to at most 12% of the customers, what should the amount of expenditure be above which a customer would receive a free gift? 2) In a sample of 100 customers, what is the number of customers whose expenditure is between 420 L.E and 485 L.E? 3) What is a probability of selecting a customer whose expenditure is differ than the population mean expenditure by at most 50 L.E? 4) What is the percentage of customers whose expenditure is at least 450 L.E.?
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 management of a supermarket wants to adopt a new promotional policy of giving free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditure for all customers at this supermarket will be
1) If the management wants to give free gifts to at most 12% of the customers, what should the amount of expenditure be above which a customer would receive a free gift?
2) In a sample of 100 customers, what is the number of customers whose expenditure is between 420 L.E and 485 L.E?
3) What is a probability of selecting a customer whose expenditure is differ than the population mean expenditure by at most 50 L.E?
4) What is the percentage of customers whose expenditure is at least 450 L.E.?
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