According to the data, the mean quantitative score on a standardized test for female college-bound high school seniors was 500 . The scores are approximately Normally distributed with a population standard deviation of 50 . A scholarship committee wants to give awards to college-bound women who score at the 97 th percentile or above on the test. What score does an applicant need? Include a well-labeled Normal curve as part of your answer.
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!
According to the data, the mean quantitative score on a standardized test for female college-bound high school seniors was
The scores are approximately
A scholarship committee wants to give awards to college-bound women who score at the
percentile or above on the test. What score does an applicant need? Include a well-labeled Normal curve as part of your answer.
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