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 μ = 6150and estimated standard deviation σ =2200. 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 not normal.Theprobability distribution of x is approximately normal withμx = 6150 andσx =1555.63.     The probability distributionof x is approximately normal withμx = 6150 andσx = 2200.The probability distributionof x is approximately normal withμx = 6150 andσx = 1100.00.
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 decreased as n increased.Theprobabilities increased as nincreased.     The probabilities stayedthe same as 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 an extremely rare event for a person to have two orthree tests 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 acommon event for a person to have two or three tests below 3,500purely by chance. The person probably has 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.
