3) Disney World requires that people employed as mickey mouse characters must have a height between 56in and 62 in. Suppose mens heights are normally dis- tributed with a mean of 68.6in and a standard deviation of 2.8 in. Suppose women heights are normally distributed with a mean of 63.7in and a standard deviation of 2.9 in. a) Find the percentage of men meeting the height requirement. b) If the height requirement is changed to exclude the tallest 50% of men and the shortest 5% of men, what are the new height requirements? 4) Out of the following, which are biased estimators of their corresponding popula- tion parameters? Sample mean, sample variance, sample range, sample standard deviation, sample proportion
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!
3) Disney World requires that people employed as mickey mouse characters must have a height between 56in and 62 in. Suppose mens heights are normally dis- tributed with a mean of 68.6in and a standard deviation of 2.8 in. Suppose women heights are
a) Find the percentage of men meeting the height requirement.
b) If the height requirement is changed to exclude the tallest 50% of men and the shortest 5% of men, what are the new height requirements?
4) Out of the following, which are biased estimators of their corresponding popula- tion parameters?
Sample mean, sample variance, sample
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