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

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).