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 = 6950 and estimated standard deviation σ = 2650. 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 not normal. The probability distribution of x is approximately normal with μx = 6950 and σx = 1873.83. The probability distribution of x is approximately normal with μx = 6950 and σx = 1325.00. The probability distribution of x is approximately normal with μx = 6950 and σx = 2650. 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 decreased as n increased. The probabilities stayed the same as n increased. The probabilities increased 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 does not have 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 has 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. 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)

The z-score for X = 3500 is

So the probability that, on a single test, x is less than 3500 is

(b)

The sampling distribution of sample mean will be approximatey distributed with mean

and standard deviation

The z-score for is

So the requried probability is

(c)

The sampling distribution of sample mean will be approximatey distributed with mean

and standard deviation

The z-score for is

So the requried probability is

(d)

The probabilities decreased as n increased.

(e)

.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.