The weight of a sophisticated running shoe is normally distributed with a mean of 12 ounces and a standard deviation of 0.5 ounces. a. What is the probability that a shoe weighs more than 13 ounces? b. What must the standard deviation of weight be in order for the company to state that 99.9% of its shoes are less than 13 ounces?
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 weight of a sophisticated running shoe is
and a standard deviation of 0.5 ounces.
a. What is the
b. What must the standard deviation of weight be in order for the company to state that 99.9%
of its shoes are less than 13 ounces?
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