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 μ = 6750 and estimated standard deviation σ = 2250. 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 μ_x = 6750 and σ_x = 1590.99.   

c. The probability distribution of x is approximately normal with μ_x = 6750 and σ_x = 2250.

d. The probability distribution of x is approximately normal with μ_x = 6750 and σ_x = 1125.00.

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 has leukopenia.

b. 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.

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 has leukopenia.

d. 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.

Answer 1

a)

μ=6750, σ=2250, n=1

We need to compute

The corresponding z-value needed to be computed:

Therefore,

b)

μ=6750, σ=2250, n=2

We need to compute   .

The corresponding z-value needed to be computed:

Therefore,

c)

μ=6750, σ=2250, n=3

We need to compute ) .

The corresponding z-value needed to be computed:

Therefore,

d)

evidently as we observe above pattern we can clearly say that The probabilities decreased as n increased Hence

c. The probabilities decreased as n increased

e)

d) 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.

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