The average weight of a young teen boy is 97 pounds with a standard deviation of 10.5 pounds. Suppose we randomly select 26 young teen boys and weigh them. The measurements (in pounds) are F1, F2, , F26. Let S = F1 + F2 + ...+F26 and let M = S/26. This means S is the sample sum and M is the sample mean of the selected teen boys (Note: random selection means F1 F26 are independent.). Assume the Fis are normally distributed. a) What is the probability that F1 > 100? b) What is the expected value of S? c) What is the standard deviation of S?
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!
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