Let x be a random variable that represents white bloodcell count per cubic milliliter of whole blood. Assume thatx has a distribution that is approximately normal, withmean ? = 6150 and estimated standard deviation ?= 2750. A test result of x < 3500 is an indication ofleukopenia. This indicates bone marrow depression that may be theresult of a viral infection.

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


(b) Suppose a doctor uses the average x for two teststaken about a week apart. What can we say about the probabilitydistribution of x?

The probability distribution of x is approximatelynormal with ?_x = 6150 and?_x = 2750.The probability distributionof x is approximately normal with?_x = 6150 and?_x =1944.54.    The probability distribution ofx is approximately normal with?_x = 6150 and?_x = 1375.00.The probabilitydistribution of x is not normal.

What is the probability of x < 3500? (Round your answerto 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 theprobabilities change as n increased?

The probabilities increased as n increased.Theprobabilities decreased as nincreased.    The probabilities stayed the sameas n increased.

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

It would be a common event for a person to have two or threetests below 3,500 purely by chance. The person probably hasleukopenia.It would be a common event for a person to have two orthree tests below 3,500 purely by chance. The person probably doesnot have leukopenia.    It would be anextremely rare event for a person to have two or three tests below3,500 purely by chance. The person probably does not haveleukopenia.It would be an extremely rare event for a person to havetwo or three tests below 3,500 purely by chance. The personprobably has leukopenia.