Standing eye heights of women are normally distributed with a mean of 1516 mm and a standard deviation of 63 mm (based on anthropometric survey data from Gordon, Churchill, et al.). a.) A door peephole is placed at a height that is uncomfortable for women with standing eye heights greater than 1605 mm. What percentage of women will find that height uncomfortable? b.) In selecting the height of a new door peephole, the architect wants its height to be suitable for the highest 99% of standing eye heights for women. What standing eye height of women separates the highest 99% from the lowest 1%? c.) What percentage of women have a standing eye height between 1420 mm and 1560 mm?
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!
1.) Standing eye heights of women are
deviation of 63 mm (based on anthropometric survey data from Gordon, Churchill, et al.).
a.) A door peephole is placed at a height that is uncomfortable for women with standing eye heights
greater than 1605 mm. What percentage of women will find that height uncomfortable?
b.) In selecting the height of a new door peephole, the architect wants its height to be suitable for the
highest 99% of standing eye heights for women. What standing eye height of women separates the
highest 99% from the lowest 1%?
c.) What percentage of women have a standing eye height between 1420 mm and 1560 mm?
d.) What is the probability that a group of twenty women have an average standing eye height that is
less than 1500 mm? Even though our sample size is less than thirty, why can the Central Limit Theorem
still apply here?
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I am not understanding what the (normal dist excel) info is and where these numbers come from? and I am not sure what table these numbers come from? when I look at positive z-score table at 0.9-----and go to the last one of .09 it's .8389? Confused.
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