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=54and estimated standard deviation=23. 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 not normal.

The probability distribution ofxis approximately normal with_x= 54 and_x= 23.

The probability distribution ofxis approximately normal with_x= 54 and_x= 16.26.

The probability distribution ofxis approximately normal with_x= 54 and_x= 11.50.

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.)