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 *?* = 6600 and estimated standard deviation *?*
= 2350. 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*?

A. The probability distribution of *x* is not normal.

B. The probability distribution of *x* is approximately
normal with *?*_{x} = 6600 and
*?*_{x} =
1175.00.

C. The probability distribution of *x* is approximately
normal with *?*_{x} = 6600 and
*?*_{x} = 2350.

D. The probability distribution of *x* is approximately
normal with *?*_{x} = 6600 and
*?*_{x} = 1661.70.

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?

A. The probabilities stayed the same as *n*
increased.

B. The probabilities increased as *n*
increased.

C. The probabilities decreased as *n* increased.

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

A. 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.

B. 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.

C. 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.

D. 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)

P(X<3500)=P(Z<(3500-6600)/2350)=P(Z<-1.32)=0.0934

b)D. The probability distribution of x is approximately normal with ?x = 6600 and ?x = 1661.70.

P(Xbar<3500)=P(Z<(3500-6600)/1661.70)=P(Z<-1.87)=0.0307

c)P(Xbar<3500)=P(Z<(3500-6600)/1661.70)=P(Z<-2.28)=0.0113

d)

C. The probabilities decreased as n increased.

B. 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.

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