Question

The weight of male american between the ages 18 to 25 is normally distributed, with mean of 162.7 lb and a standard deviation of 28 lb. One definition of obesity states that a person is obese if the z-score of his or her weight is greater than 2. What is the obesity threshold weight for a young adult american male? Round your answer to the nearest tenth.

Answer 1

218.7 lb.

Explanation:

We have been given that the weight of male american between the ages 18 to 25 is normally distributed, with mean of 162.7 lb and a standard deviation of 28 lb.

One definition of obesity states that a person is obese if the z-score of his or her weight is greater than 2.

We will use z-score formula to solve our given problem.

`z=(x-\mu)/(\sigma)`, where,

`z=\text{ z-score}`,

`x=\text{ Random sample-score}`,

`\mu=\text{ Mean}`,

`\sigma=\text{ Standard deviation}`.

Upon substituting our given values in z-score formula we will get,

`2=(x-162.7)/(28)`

Now let us solve for x.

Upon multiplying both sides of our equation by 28 we will get,

`2*28=(x-162.7)/(28)*28`

`56=x-162.7`

Let us add 162.7 to both sides of our equation.

`56+162.7=x-162.7+162.7`

`218.7=x`

Therefore, the obesity threshold weight for a young adult American male is 218.7 pounds.