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 = 6100 and estimated standard deviation σ = 2850. 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 = 6100 and σ_x = 2015.25.

The probability distribution of x is approximately normal with μ_x = 6100 and σ_x = 2850.   

The probability distribution of x is approximately normal with μ_x = 6100 and σ_x = 1425.00.

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 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.  

  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 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.

Answer 1

a)

                                  

                                   = P(Z < -0.91)

                                   = 0.1814

b)

Option-A) The probability distribution of x is approximately normal with μ_x = 6100 and σ_x = 2015.25.

                             

                              = P(Z < -1.29)

                              = 0.0985

c)

                                  

                                   = P(Z < -1.58)

                                   = 0.0571

d) Option-B) The probabilities decreased as n increased.

Option-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 has leukopenia.