A 1987 study found that the distribution of weights for the population of males in the United States was approximately normally distributed with mean µ = 172.2 pounds and standard deviation σ = 29.8 pounds. (a) Create a rough sketch of this Normal distribution, by hand. It doesn’t have to look perfect. However, make sure that the general shape is correct, and that you have labelled the mean and the standard deviation somewhere in your figure. (b) By hand, approximate the probability that a randomly selected man (in 1987) weighs more than 202.0 pounds. (c) By hand, approximately how much would a man have to weigh (in 1987) in order to be in the 2.5th percentile of male weights? (Note: An individual is said to be “in the 2.5th percentile” if 2.5% of individuals weigh less than him.) (d) The same study found that the average weight of women in the sample was 144.2 pounds. Use R JupyterHub to find the probability that a randomly chosen man (in 1987) weighs more than this amount.
A 1987 study found that the distribution of weights for the population of males in the United States was approximately
(a) Create a rough sketch of this Normal distribution, by hand. It doesn’t have to look perfect. However, make sure that the general shape is correct, and that you have labelled the mean and the standard deviation somewhere in your figure.
(b) By hand, approximate the probability that a randomly selected man (in 1987) weighs more than 202.0 pounds.
(c) By hand, approximately how much would a man have to weigh (in 1987) in order to be in the 2.5th percentile of male weights? (Note: An individual is said to be “in the 2.5th percentile” if 2.5% of individuals weigh less than him.)
(d) The same study found that the average weight of women in the sample was 144.2 pounds. Use R JupyterHub to find the probability that a randomly chosen man (in 1987) weighs more than this amount.
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