The distribution of weights for 12–month–old baby boys in the US is approximately normal with mean µ = 22.5 pounds and standard deviation σ = 2.2 pounds. a) If a 12–month–old boy weighs 20.3 pounds, approximately what weight percentile is he in? b) If a 12–month–old boy is in the 84th percentile in weight, estimate his weight. c) Estimate the weight of a 12–month–old boy who is in the 25th percentile by weight. d) Estimate the weight of a 12–month–old boy who is in the 75th percentile by weight.
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 distribution of weights for 12–month–old baby boys in the US
is approximately normal with mean µ = 22.5 pounds and standard
deviation σ = 2.2 pounds.
a) If a 12–month–old boy weighs 20.3 pounds, approximately what
weight percentile is he in?
b) If a 12–month–old boy is in the 84th percentile in weight, estimate
his weight.
c) Estimate the weight of a 12–month–old boy who is in the 25th
percentile by weight.
d) Estimate the weight of a 12–month–old boy who is in the 75th
percentile by weight.
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