35 48 61 74 87 100 113 Distribution of College Algebra Course Grades What is the mean of this normal distribution?
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!
The normal distribution is a type of continuous distribution where most of the data lies in the center and a few of the data lie at its ends. It is asymmetric distribution and is bell-shaped with a single peak at the center.
The normal distribution is completely described by its two parameters, the mean and the standard deviation. The mean is responsible for the location of the center whereas the standard deviation measures the spread of the curve.
The curve represents that the mean is 74. Calculate the standard deviation as:
Lower limit = Mean - 1 * Standard deviation
61 = 74-1*Standard deviation
Standard deviation = 13
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