Question

Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean ? = 6600 and estimated standard deviation ? = 2350. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection.

(a) What is the probability that, on a single test, x is less than 3500? (Round your answer to four decimal places.)

(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x?

A. The probability distribution of x is not normal.

B. The probability distribution of x is approximately normal with ?_x = 6600 and ?_x = 1175.00.    

C. The probability distribution of x is approximately normal with ?_x = 6600 and ?_x = 2350.

D. The probability distribution of x is approximately normal with ?_x = 6600 and ?_x = 1661.70.

What is the probability of x < 3500? (Round your answer to four decimal places.)


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


(d) Compare your answers to parts (a), (b), and (c). How did the probabilities change as n increased?

A. The probabilities stayed the same as n increased.

B. The probabilities increased as n increased.    

C. The probabilities decreased as n increased.

If a person had x < 3500 based on three tests, what conclusion would you draw as a doctor or a nurse?

A. It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia.

B. It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia.

C. It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia.

D. It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia.

Answer 1

a)

P(X<3500)=P(Z<(3500-6600)/2350)=P(Z<-1.32)=0.0934

b)D. The probability distribution of x is approximately normal with ?x = 6600 and ?x = 1661.70.

P(Xbar<3500)=P(Z<(3500-6600)/1661.70)=P(Z<-1.87)=0.0307

c)P(Xbar<3500)=P(Z<(3500-6600)/1661.70)=P(Z<-2.28)=0.0113

d)

C. The probabilities decreased as n increased.

B. It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia.