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 = 6700 and estimated standard deviation σ = 2700. 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 = 6700 and σ_x = 1350.00.The probability distribution of x is approximately normal with μ_x = 6700 and σ_x = 2700.     The probability distribution of x is not normal.The probability distribution of x is approximately normal with μ_x = 6700 and σ_x = 1909.19.

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 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.     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

a)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	6700
std deviation   =σ=	2700.0000

probability =

P(X<3500)

=

P(Z<-1.19)=

0.1170

b)

The probability distribution of x is approximately normal with μ_x = 6700 and σ_x = 1909.19.

probability =

P(X<3500)

=

P(Z<-1.68)=

0.0465

c)

sample size       =n=	3
std error=σx̅=σ/√n=	1558.8457

probability =

P(X<3500)

=

P(Z<-2.05)=

0.0202

d)

The probabilities decreased as n increased.

t 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