In 1988, on the math SAT, the males taking the exam averaged about 500, while the females averaged about 455. Both histograms followed the normal curve, and both standard deviations were about 100. Estimate the percentage of males in 1988 scoring over 600 Estimate the percentage of females in 1988 scoring over 600. What is the 10th percentile of the scores for the males? What is the first quartile of the scores for the females?
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!
In 1988, on the math SAT, the males taking the exam averaged about 500, while the females averaged about 455. Both histograms followed the normal curve, and both standard deviations were about 100.
Estimate the percentage of males in 1988 scoring over 600
Estimate the percentage of females in 1988 scoring over 600.
What is the 10th percentile of the scores for the males?
What is the first
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