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 = 6150 and estimated standard deviation σ = 2750. 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?

The probability distribution of x is approximately normal with μ_x = 6150 and σ_x = 2750.The probability distribution of x is approximately normal with μ_x = 6150 and σ_x = 1944.54.    The probability distribution of x is approximately normal with μ_x = 6150 and σ_x = 1375.00.The probability distribution of x is not normal.

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?

The probabilities increased as n increased.The probabilities decreased as n increased.    The probabilities stayed the same as n increased.

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

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.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.    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.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.

Answer 1

a) Approximately, X ~ Normal(6150, 2750²)

The probability that, on a single test, x is less than 3500 is = 0.167614

b) Let denotes the average white blood cell count per cubic milliliter of whole blood for a random sample of 2 tests.

The probability distribution of x is approximately normal with μ_x = 6150 and σ_x = 1944.54.

c) Let denotes the average white blood cell count per cubic milliliter of whole blood for a random sample of 3 tests.

The probability distribution of x is approximately normal with μ_x = 6150 and σ_x = 1587.71.

d) The probabilities decreased as n increased.