Question

heights of men on a basketball team have a bell shaped distribution with the mean of 177 cm and a standard deviation if 5 cm. using the empirical rule, what is the approximate percentage of the men between 162 cm and 192 cm?

Answer 1

The variable

X: height of a basketball team

This variable has a bell shaped distribution (Normal distribution) with mean μ=177cm and a standard deviation of δ=5cm

The empirical rule states that

68% of the distribution is within one standard deviation away from the mean

`\begin{gathered} \mu\pm\sigma=0.68 \\ 177\pm5 \\ (172;182) \end{gathered}`

95% of the distribution is within two standard deviations away from the mean

`\begin{gathered} \mu\pm2\sigma=0.95 \\ 177\pm2\cdot5 \\ (167,187) \end{gathered}`

99.7% of the distribution is within three standard deviations away from the mean

`\begin{gathered} \mu\pm3\sigma=0.997 \\ 177\pm3\cdot5 \\ (162,192) \end{gathered}`

So, following the empirical rule, 99.7% of the men are between 162 cm and 192 cm