Consider the normal distribution defined by the figure to the right. Find the mean μ and standard deviation σ of the distribution. A normal curve is over a horizontal axis. A vertical line segment extends from the horizontal axis to the curve at the center, a vertical line segment extends from the horizontal axis at 54 to Upper P prime on the curve and a vertical line segment extends from the horizontal axis at 62 to P on the curve, where 54 is to the left of center and 62 is to the right of center. The area under the curve between 54 and 62, is labeled 68% of the data and is shaded.6254 μ= (Simplify your answer.)
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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Consider the
μ
and standard deviation
σ
of the distribution. |
A normal curve is over a horizontal axis. A vertical line segment extends from the horizontal axis to the curve at the center, a vertical line segment extends from the horizontal axis at 54 to Upper P prime on the curve and a vertical line segment extends from the horizontal axis at 62 to P on the curve, where 54 is to the left of center and 62 is to the right of center. The area under the curve between 54 and 62, is labeled 68% of the data and is shaded.6254
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