The Acme Company manufactures widgets. The distribution of widget weights is approximately normal with a mean of 57 ounces and a standard deviation of 11 ounces. Use the Empirical Rule to answer the questions below. Sketch the distribution in order to answer these questions. (a) 99.7% of the widget weights lie between and (b) What percentage of the widget weights lie between 46 and 90 ounces? % (c) What percentage of the widget weights lie below 79 ? %
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 Acme Company manufactures widgets. The distribution of widget weights is approximately normal with a
Use the
(a) 99.7% of the widget weights lie between and
(b) What percentage of the widget weights lie between 46 and 90 ounces? %
(c) What percentage of the widget weights lie below 79 ? %
Empirical Rule :
The empirical rule has some powerful advantages when we are working with a population that follows the normal distribution. Whitt eh empirical rule we can determine intervals that contain 68 percent, 95 percent, and 99.7 percent of the data using the following formulas respectively:
Note that,
percent of data lies on either side of the interval.
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