Suppose that a highly selective college desires to admit students based on their performance on an entrance exam. The grades on the exam are normally distributed with a mean of 1,000 and a standard deviation of 200. If the college wants to admit only those whose grades are in the top 1.5%, what is the minimum grade that an applicant must get on the exam in order to be admitted?
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!
Suppose that a highly selective college desires to admit
students based on their performance on an entrance exam.
The grades on the exam are
mean of 1,000 and a standard deviation of 200. If the college
wants to admit only those whose grades are in the top 1.5%,
what is the minimum grade that an applicant must get on
the exam in order to be admitted?
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