The results of the nationwide aptitude test in Mathematics are normally distributed with mean = 80, and standard deviation=15. What is the percentile rank of the score 84?
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!
![There are three grades in a report card that you want to interpret
in terms of performance: Mathematics(75), English(85), Science( 90).
The means are 72, 83, and 88 respectively. The standard deviations
are 3, 10, and 15 respectively. Is the information sufficient for you to
compare thye grades? If so, discuss your processes. If not, explain
why it is impossible.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F13aa0de8-23b1-4e30-a2ab-8af87497eddb%2F728a06f5-d4cd-42fd-8164-779f170ccf34%2Ffo2qmsv_processed.png&w=3840&q=75)
![The results of the nationwide aptitude test in Mathematics are
normally distributed with mean = 80, and standard deviation=15. What
is the percentile rank of the score 84?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F13aa0de8-23b1-4e30-a2ab-8af87497eddb%2F728a06f5-d4cd-42fd-8164-779f170ccf34%2F7bpk9ho_processed.png&w=3840&q=75)
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