Question

To study bonding between mothers and infants, a researcher places each mother and her infant in a playroom and has the mother leave for 10 minutes. The records crying time in the sample of infants during this time that the mother was not present and finds that erying time is normally distributed with M-8 and SO 1.3, Based on the empirical rule, state the range of crying times within 68% of infants cried, 95% of infants cried and 99.7% of infants cried. (a) 68% of infants cried X to 1.4 x min (b) 95% of infants cried to (c) 99.7% of infants cried to min Make sure you identify the outoff values at the first, second, and third standard Section 4.1

Answer 1

${\color{Blue} \mathbf{Solution}}$

$\mathbf{given}:\;Mean\;(\mu)=8,\;standard\;deviation\;(SD)=1.3$

$\mathbf{Accroding\; to\; empirical \;rule,}$

$M-3*SD=8-(3*1.3)=\mathbf{4.1}$

$M-2*SD=8-(2*1.3)=\mathbf{5.4}$

$M-1*SD=8-(1*1.3)=\mathbf{6.7}$

$M=\mathbf{8}$

$M+1*SD=8+(1*1.3)=\mathbf{9.3}$

$M+2*SD=8+(2*1.3)=\mathbf{10.6}$

$M+3*SD=8-(3*1.3)=\mathbf{11.9}$

${\color{Blue} \mathbf{(a)}}\;68\%\; of \;infants\; cried$

$\mathbf{{\color{Red} 6.7}}\;\;to\;\;\mathbf{{\color{Red} 9.3}}$

${\color{Blue} \mathbf{(b)}}\;95\%\; of \;infants\; cried$

$\mathbf{{\color{Red} 5.4}}\;\;to\;\;\mathbf{{\color{Red} 10.6}}$

${\color{Blue} \mathbf{(c)}}\;99.7\%\; of \;infants\; cried$

$\mathbf{{\color{Red} 4.1}}\;\;to\;\;\mathbf{{\color{Red} 11.9}}$