Question

Suppose a normally distributed set of data has a mean of 172 and a standard deviation of 15. Use the 68-95-99.7 rule to determine the percent of scores in the data set expected to be between the scores 142 and 187. Give your answer in decimal form and keep all decimal places throughout your calculations and in your final answer.

Answer 1

$\dpi{100} \mathbf{Solution}$

$\dpi{100} \mathbf{Answer:}$

$\dpi{100} {\color{Red} \mathbf{0.815}}$

$\dpi{100} \mathbf{given:}\;\mu=172,\;\sigma=15$

$\dpi{100} \mathbf{Use\;68-95-99.7\; rule}$

$\dpi{100} \mu-3\sigma=172-(3*15)=\mathbf{127}$

$\dpi{100} \mu-2\sigma=172-(2*15)=\mathbf{142}$

$\dpi{100} \mu-1\sigma=172-(1*15)=\mathbf{157}$

$\dpi{100} \mu=\mathbf{172}$

$\dpi{100} \mu+1\sigma=172+(1*15)=\mathbf{187}$

$\dpi{100} \mu+2\sigma=172+(2*15)=\mathbf{202}$

$\dpi{100} \mu+3\sigma=172+(3*15)=\mathbf{217}$

0.15 0.15% 2.35%/ 13.5%། 34%། 34% ཡང་ དང་ བ་ དང༌། དབང་དུས་ 13.5% 2.35% 202217 142157132137 68% 95% 99.7%

$\dpi{100} \mathbf{P(between \;142\;and\;187)=13.5\%+34\%+34\%=81.5\%\approx {\color{Red} \mathbf{0.815}}}$

$\dpi{100} \mathbf{Percent \:of \:scores\: in \:the\: data \:set \:expected\: to \:be\: between\: the \:scores\: 142\: and \:187\:is\;{\color{Red} 0.815}}$