Dice. When one die is rolled, the number of spots show-ing has a mean of 3.5 and a standard deviation of 1.7. Suppose you roll 10 dice. What’s the approximate prob-ability that your total is between 30 and 40 (that is, the average for the 10 dice is between 3 and 4)? Specify themodel you use and the assumptions and conditions thatjustify your approach.
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!
ing has a
ability that your total is between 30 and 40 (that is, the
model you use and the assumptions and conditions that
justify your approach.
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