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 ? = 7950 and estimated standard deviation ? = 2600. 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 ?_x = 7950 and ?_x = 2600.The probability distribution of x is approximately normal with ?_x = 7950 and ?_x = 1300.00.    The probability distribution of x is approximately normal with ?_x = 7950 and ?_x = 1838.48.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 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 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 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 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

a) probability that, on a single test, x is less than 3500 =P(X<3500)=P(Z<(3500-7950)/2600)=P(Z<-1.71)

=0.0436 ( please try 0.0435 if this comes wrong)

b)

probability distribution of x is approximately normal with ?x = 7950 and ?x = 1838.48

P(Xbar<3500)=P(Z<(3500-7950)/(2600/sqrt(2))=0.0078( please try 0.0077 if this comes wrong)

c)

P(Xbar<3500)=P(Z<(3500-7950)/(2600/sqrt(3))=0.0015

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 has leukopenia