Scores on an exam required for all medical school applicants were approximately Normal with a mean score of 487 and a standard deviation of 9.1. Complete parts (a) and (b) below. a. Suppose an applicant had a test score of 502. What percentile corresponds with this score? % (Round to the nearest integer as needed.) b. Suppose to be considered at a highly selective school an applicant should score in the top 8% of all test takers. What score would place an applicant in the top 8%? (Round to the nearest integer as needed.)
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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