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

Answer:

218.7 lb.

Step-by-step 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.

$z=\frac{x-\mu}{\sigma}$, 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,

$2=\frac{x-162.7}{28}$

Now let us solve for x.

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

$2*28=\frac{x-162.7}{28}*28$

$56=x-162.7$

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.

Answer 2

Answer: 218.7 lbs

Step-by-step explanation: apex