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.
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
[tex]z=\text{ z-score}[/tex],
[tex]x=\text{ Random sample-score}[/tex],
[tex]\mu=\text{ Mean}[/tex],
[tex]\sigma=\text{ Standard deviation}[/tex].
Upon substituting our given values in z-score formula we will get,
[tex]2=\frac{x-162.7}{28}[/tex]
Now let us solve for x.
Upon multiplying both sides of our equation by 28 we will get,
[tex]2*28=\frac{x-162.7}{28}*28[/tex]
[tex]56=x-162.7[/tex]
Let us add 162.7 to both sides of our equation.
[tex]56+162.7=x-162.7+162.7[/tex]
[tex]218.7=x[/tex]
Therefore, the obesity threshold weight for a young adult American male is 218.7 pounds.
