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 = 6950 and estimated standard deviation σ = 2650. 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 not normal.The probability distribution of x is approximately normal with μ_x = 6950 and σ_x = 1873.83.    The probability distribution of x is approximately normal with μ_x = 6950 and σ_x = 1325.00.The probability distribution of x is approximately normal with μ_x = 6950 and σ_x = 2650.

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 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 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 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.

Answer 1

Here we have : μ = 6950 , σ = 2650.

a) We need to find,

p ( x < 3500 )

= p ( z < -1.30 )

= 0.9032 ---Look in the standard normal probability table for z value -1.3 and 0.00.

b) Here n = 2

So = 6950 and =

We need to find

= p ( z < -1.84 )

= 0.0329 --- look in the standard normal probability table for z value -1.8 and 0.04 .

c) n = 3

So = 6950 and =

We need to find

= p ( z < -2.25 )

= 0.0122 --- look in the standard normal probability table for z value -2.2 and 0.05 .

d) Here probabilities are decreased as n increased.

Conclusion : 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.