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 μ_x = 6750 andσ_x = 1590.99.   

c. The probability distribution of x is approximatelynormal with μ_x = 6750 andσ_x = 2250.

d. The probability distribution of x is approximatelynormal with μ_x = 6750 andσ_x = 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.    

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.