7.3 Central Limit Theorem: Finding Probability A population of values has a normal distribution with u = 72.9 and o = 60.1. You intend to draw a random sample of size n= 192. a.) Find the probability that a single randomly selected value is between 66.8 and 77.2. P(66.8 < X< 77.2) = b.) Find the probability that a sample of stze n = 192 is randomly selected with a mean between 66.8 and 77.2. P(66.8 < M < 77.2)% = Enter your answers as numbers accurate to 4 decimal places.
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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