11.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=71and estimated standard deviation=44. 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 7.1.

• The probability distribution ofxis approximately normal with_x= 71 and_x= 44.
• The probability distribution ofxis not normal.
• The probability distribution ofxis approximately normal with_x= 71 and_x= 22.00.
• The probability distribution ofxis approximately normal with_x= 71 and_x= 31.11.

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