Engineers must consider the breadths of heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.3 inches and a standard deviation of 1.2 inches. Due to financial constraints, the helmets will be designed to fit everyone except those with head breadths that are in the smallest 3.3% or largest 3.3%. What is the minimum head breadth that will fit the clientele? What is the maximum head breadth that will fit the clientele?
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!
Engineers must consider the breadths of heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are
What is the minimum head breadth that will fit the clientele?
What is the maximum head breadth that will fit the clientele?
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