The height of an 8th grader is modeled using the normal distribution shown below. The mean of the distribution is 62.7 in and the standard deviation is 1.8 in. In the figure, V is a number along the axis and is under the highest part of the curve. And, U and W are numbers along the axis that are each the same distance away from V. Use the empirical rule to choose the best value for the percentage of the area under the curve that is shaded, and find the values of U, V, and W. Percentage of total area shaded: (Choose one) ▼ 56 58 60 U 62 V 64 W 66 68 Height (in inches) W
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 height of an 8th grader is modeled usingthe normal distribution shown below.
The mean of the distribution is 62.7 in and the standard deviation is 1.8 in.
In the figure, V is a number along the axis and is under the highest part of the curve.
And, U and W are numbers along the axis that are each the same distance away from V.
Use the empirical rule to choose the best value for the percentage of the area under the curve that is shaded, and find the values of U, V, and W.
Percentage of total area shaded:
(Choose one) ▼
56
58
60
U
62
V
64 W
66
68
Height (in inches)
w =]
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