The ages of the members of a gym have a bell-shaped distribution with a mean of 48 years and a standard deviation of 11 years. Based on the empirical rule, what should you predict about the percentage of gym members aged between 26 and 70?

Based on the empirical rule, we could predict that the percentage of gym members aged between 26 and 70 is about 95%Further explanationThe probability of an event is defined as the possibility of an event occurring against sample space.Let us tackle the problem.[tex]\texttt{ }[/tex]Empirical Rule of Normal Distribution :[tex]\left[\begin{array}{ccc}Interval&Empirical Rule\\\overline{x} \pm\sigma&68 \%\\\overline{x} \pm 2\sigma&95 \%\\\overline{x} \pm 3\sigma&99.7 \%\end{array}\right][/tex]where: [tex]\overline{x}[/tex] = mean[tex]\sigma[/tex] = standard deviation[tex]\texttt{ }[/tex]The ages of the members of a gym have a bell-shaped distribution with a mean of 48 years and a standard deviation of 11 years.[tex]\overline{x} = 48[/tex] and [tex]\sigma = 11[/tex]The percentage of gym members aged between 26 and 70 :[tex]26 = 48 - 22 = 48 - 2(11) = \overline{x} - 2\sigma[/tex][tex]70 = 48 + 22 = 48 + 2(11) = \overline{x} + 2\sigma[/tex]Based on Empirical Rule we can conclude that :The percentage of gym members aged between 26 and 70 [tex]( \overline{x} \pm 2\sigma)[/tex] will be approximately 95%[tex]\texttt{ }[/tex]Learn moreDifferent Birthdays : or Independent Events : exclusive : detailsGrade: High SchoolSubject: MathematicsChapter: ProbabilityKeywords: Probability , Sample , Space , Six , Dice , Die , Normal , Distribution , Bell - Shaped , Empirical Rule , Prediction , Standard Deviation , Mean , Gym , Members , Ages , Rule , Average