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%

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

Let us tackle the problem.

Empirical Rule of Normal Distribution :

where:

= mean

= standard deviation

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.

and

The percentage of gym members aged between 26 and 70 :

Based on Empirical Rule we can conclude that :

The percentage of gym members aged between 26 and 70 will be approximately 95%

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