1.According to the Centers for Disease Control, about 36% of U.S. adults were obese in 2013. To see if that has changed since the last study, a random sample of 250 U.S. adults will be
checked.
a. Describe the sampling distribution model for the sample proportion (assuming no change
in obesity rates) by naming the model and telling its mean and standard deviation. Justify
your answer.
b. Sketch and clearly label the model.
c. What is the probability that in this group less than 25% of the adults will be found to be
obese?

Both the parts of this question require the use of the "Intersecting Secant-Tangent Theorem".

Part A

The definition of the Intersecting Secant-Tangent Theorem is:

"If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment."

This, when applied to our case becomes, "The length of the secant RT, times its external segment, ST, equals the square of the tangent segment TU".

Mathematically, it can be written as:

Part B

It is given that RT = 9 in. and ST = 4 in. Thus, it is definitely possible to find the value of the length TU and it can be found using the Intersecting Secant-Tangent Theorem as:

Thus,

Thus the length of TU=6 inches