For each of the scenarios below, answer whether or not it can be represented by a binomial distribution. If it can, explain why it meets the criteria for a binomial distribution. If it cannot, explain why it fails to meet the criteria for a binomial distribution. a. A geologist randomly pulls a stone from their collection and identifies it as Igneous, Sedimentary, or Metamorphic. b. A nutritionist will randomly select different types of sugar-free ice cream until they find one that tastes acceptable.
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!
1. For each of the scenarios below, answer whether or not it can be represented by a binomial distribution. If it can, explain why it meets the criteria for a binomial distribution. If it cannot, explain why it fails to meet the criteria for a binomial distribution.
a. A geologist randomly pulls a stone from their collection and identifies it as
Igneous, Sedimentary, or Metamorphic.
b. A nutritionist will randomly select different types of sugar-free ice cream until they find one that tastes acceptable.
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