Heights of 10 year old children, regardless of sex, closely follow a normal distribution with mean 54.8 inches and standard deviation 7 inches. For parts (a) through (c), enter your responses as a decimal with 2 decimal places. a) What percentage of 10 year old children are more than 46.05 inches tall? b) What percentage of 10 year old children are less than 59 inches tall? c) What percentage of 10 year old children are between 46.05 and 59 inches tall? d) 74 % of 10 year old children are less than inches tall? (Do not round the final answer for d).)
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!
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