SAT scores (out of 2,400) are normally distributed with a mean of 1,500 and a standard deviation of 300. Suppose a school council awards a certificate of excellence to all students who score at least 1,900 on the SAT, and suppose we pick one of the recognized students at random. What is the probability this student’s score will be at least 2,100?
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!
SAT scores (out of 2,400) are
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