Question

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?

Answer 1

Based on the empirical rule, we could predict that the percentage of gym members aged between 26 and 70 is about 95%

Further explanation

The probability of an event is defined as the possibility of an event occurring against sample space.

Let us tackle the problem.

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Empirical Rule of Normal Distribution :

$\left[\begin{array}{ccc}Interval&Empirical Rule\\\overline{x} \pm\sigma&68 \%\\\overline{x} \pm 2\sigma&95 \%\\\overline{x} \pm 3\sigma&99.7 \%\end{array}\right]$

where:

$\overline{x}$ = mean

$\sigma$ = standard deviation

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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.

$\overline{x} = 48$ and $\sigma = 11$

The percentage of gym members aged between 26 and 70 :

$26 = 48 - 22 = 48 - 2(11) = \overline{x} - 2\sigma$

$70 = 48 + 22 = 48 + 2(11) = \overline{x} + 2\sigma$

Based on Empirical Rule we can conclude that :

The percentage of gym members aged between 26 and 70 $( \overline{x} \pm 2\sigma)$ will be approximately 95%

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Learn more

• Different Birthdays : brainly.com/question/7567074
• Dependent or Independent Events : brainly.com/question/12029535
• Mutually exclusive : brainly.com/question/3464581

Answer details

Grade: High School

Subject: Mathematics

Chapter: Probability

Keywords: Probability , Sample , Space , Six , Dice , Die , Normal , Distribution , Bell - Shaped , Empirical Rule , Prediction , Standard Deviation , Mean , Gym , Members , Ages , Rule , Average