A large group of students took a test in Statistics and the final grades have a mean of 75 and a standard deviation of 20. If we can approximate the distribution of these grades by a normal distribution, what percent of the students a) scored between 50 and 90? b) scored higher than 90? c) should pass the test (grades≥50)? d) should fail the test (grades<50)?
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!
A large group of students took a test in Statistics and the final grades have a mean of 75 and a standard deviation of 20. If we can approximate the distribution of these grades by a
- a) scored between 50 and 90?
- b) scored higher than 90?
c) should pass the test (grades≥50)?
d) should fail the test (grades<50)?
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