Historically, the SAT score of a randomly selected student is normally distributed with a mean of 1518 points and a standard deviation of 351.7 points. Let X be the SAT score of a randomly selected student and let X be the average SAT score of a random sample of size 29. 1. Describe the probability distribution of X and state its parameters u and o: and find the probability that the SAT score of a randomly selected student is less than 1879 points. (Round the answer to 4 decimal places) 2. Use the Central Limit Theorem to describe the probability distribution of X and state its parameters Hx and ox: (Round the answers to 1 decimal place)
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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