The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 56 ounces and a standard deviation of 3 ounces. Use the Standard Deviation Rule, also known as the Empirical Rule (see image below). Do not use normalcdf on your calculator. Suggestion: 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 50 and 65 ounces? % c) What percentage of the widget weights lie above 53 ? %
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 bell-shaped. The widget weights have a mean of 56 ounces and a standard deviation of 3 ounces.
Use the Standard Deviation Rule, also known as the
Suggestion: 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 50 and 65 ounces? %
c) What percentage of the widget weights lie above 53 ? %
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