Let x represent the dollar amount spend on supermarket impulse buying in a 10-minute unplanned shopping interval. The mean of this distribution is µ=$20 and the standard deviation is =$7. If we assume the x distribution is approximately normal: (1) What is the probability that a randomly selected shopper will spend between $18 and $22? (1) Consider a random sample of n = 100 shoppers. What is the probability that is between $18 and $22? (2) State two different ways we know the distribution from part (b) is normally distributed.
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!
- Let x represent the dollar amount spend on supermarket impulse buying in a 10-minute unplanned shopping interval. The mean of this distribution is µ=$20 and the standard deviation is =$7. If we assume the x distribution is approximately normal:
- (1) What is the
probability that a randomly selected shopper will spend between $18 and $22? - (1) Consider a random sample of n = 100 shoppers. What is the probability that is between $18 and $22?
- (1) What is the
- (2) State two different ways we know the distribution from part (b) is
normally distributed.
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