To validate its claim that there are "2 scoops of raisins" in every box of Kellogg's Raisin Bran, the company hires an independent counsulting firm to count the number of raisins in 1500 randomly selected boxes. The consulting firm notes the following summary statistics: Average Number of Raisins (per box): 256 raisins Standard Deviation: 22.5 raisins a) Assuming a Normal model can be applied to the sample, explain what the 68-95-99.7% rules predicts about raisins in boxes of Raisin Bran. Answer in complete sentences. b) Use the 68-95-99.7% rule to predict the percentage of Raisin Bran boxes that have less than 211 raisins. Answer with a complete sentence
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!
To validate its claim that there are "2 scoops of raisins" in every box of Kellogg's Raisin Bran, the company hires an independent counsulting firm to count the number of raisins in 1500 randomly selected boxes. The consulting firm notes the following summary statistics:
Average Number of Raisins (per box): 256 raisins
Standard Deviation: 22.5 raisins
a) Assuming a Normal model can be applied to the sample, explain what the 68-95-99.7% rules predicts about raisins in boxes of Raisin Bran. Answer in complete sentences.
b) Use the 68-95-99.7% rule to predict the percentage of Raisin Bran boxes that have less than 211 raisins. Answer with a complete sentence.
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