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 = 8650 and estimated standard deviation σ = 2950. 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 μx = 8650 and σx = 2950.

The probability distribution of x is not normal.

The probability distribution of x is approximately normal with μx = 8650 and σx = 2085.97.

The probability distribution of x is approximately normal with μx = 8650 and σx = 1475.00.

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? The probabilities decreased as n increased. The probabilities increased 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 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.

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 a common event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia.

Answer 1

Used R for calculations. On L.H.S. is R output and on R.H.S. is R code.

a) The probability that, on a single test, x is less than 3500 is  0.0404.

(b) Suppose a doctor uses the average x for two tests taken about a week apart. the probability distribution of x is

The probability distribution of x is approximately normal with μx = 8650 and σx = 2085.97.

the probability of x < 3500 is 0.0068 .

(c)

Suppose a doctor uses the average x for three tests taken about a week apart. the probability distribution of x is

The probability distribution of x is approximately normal with μx = 8650 and σx = 1703.183

the probability of x < 3500 is 0.0012

(d) The probabilities decreased as n increased.

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.