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 = 2200. 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 μ_x = 6700 and σ_x = 1555.63.   

c.The probability distribution of x is approximately normal with μ_x = 6700 and σ_x = 1100.00.

d.The probability distribution of x is approximately normal with μ_x = 6700 and σ_x = 2200.

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 increased as n increased.

b.The probabilities stayed the same as n increased.

c.The probabilities decreased as n increased.

Answer 1

a) P(X < 3500)

= P((X - )/ < (3500 - )/)

= P(Z < (3500 - 6700)/2200)

= P(Z < -1.45)

= 0.0735

b) = = 6700

    =

          = 2200/ = 1555.63

Option - b) The probability distribution of x is approximately normal with = 6700 and = 1555.63

P( < 3500)

= P(( - )/() < (3500 - )/())

= P(Z < (3500 - 6700)/1555.63)

= P(Z < -2.06)

= 0.0197

c) = = 6700

    =

          = 2200/ = 1270.17

The probability distribution of x is approximately normal with = 6700 and = 1270.17

P( < 3500)

= P(( - )/() < (3500 - )/())

= P(Z < (3500 - 6700)/1270.17)

= P(Z < -2.52)

= 0.0059

d) Option - a) The probabilities increased as n increased.