Letxbe a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old,xhas a distribution that is approximately normal, with mean=74and estimated standard deviation=24. A test resultx<40 is an indication of severe excess insulin, and medication is usually prescribed.

(a) What is the probability that, on a single test,x<40? (Round your answer to four decimal places.)

(b) Suppose a doctor uses the averagexfor two tests taken about a week apart. What can we say about the probability distribution ofx?Hint: See Theorem 6.1.

The probability distribution ofxis approximately normal with_x= 74 and_x= 12.00.

The probability distribution ofxis approximately normal with_x= 74 and_x= 24.

The probability distribution ofxis not normal.

The probability distribution ofxis approximately normal with_x= 74 and_x= 16.97.

What is the probability thatx<40? (Round your answer to four decimal places.)

(c) Repeat part (b) forn= 3 tests taken a week apart. (Round your answer to four decimal places.)

(d) Repeat part (b) forn= 5 tests taken a week apart. (Round your answer to four decimal places.)

(e) Compare your answers to parts (a), (b), (c), and (d). Did the probabilities decrease asnincreased?

Yes

No

Explain what this might imply if you were a doctor or a nurse.

The more tests a patient completes, the weaker is the evidence for excess insulin.

The more tests a patient completes, the stronger is the evidence for lack of insulin.

The more tests a patient completes, the weaker is the evidence for lack of insulin.

The more tests a patient completes, the stronger is the evidence for excess insulin.