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 = 6750 and estimated standard deviation σ= 2250. 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?
a. The probability distribution of x is not normal.
b. The probability distribution of x is approximatelynormal with μx = 6750 andσx = 1590.99.  Â
c. The probability distribution of x is approximatelynormal with μx = 6750 andσx = 2250.
d. The probability distribution of x is approximatelynormal with μx = 6750 andσx = 1125.00.
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?
a. The probabilities stayed the same as nincreased.
b. The probabilities increased as nincreased.   Â
c. The probabilities decreased as n increased.
If a person had x < 3500 based on three tests, whatconclusion would you draw as a doctor or a nurse?
a. It would be a common event for a person to have two or threetests below 3,500 purely by chance. The person probably hasleukopenia.
b. It would be a common event for a person to have two or threetests below 3,500 purely by chance. The person probably does nothave leukopenia.
c. It would be an extremely rare event for a person to have twoor three tests below 3,500 purely by chance. The person probablyhas leukopenia.
d. It would be an extremely rare event for a person to have twoor three tests below 3,500 purely by chance. The person probablydoes not have leukopenia.
