Naijah's daily commute in to work takes an average of 19 minutes with a standard deviation of 2 minutes. Assume that her daily commute times follow a Normal distribution. Use the Empirical Rule to estimate the percentage of times that her commute will fall within the following intervals.
17 mins or less= A)2.5% B)34% C)47.5% D)16% E)68%
19 to 23 Mins= A)2.5% B)34% C)16% D)47.5% E)68%

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