Question 1052345: 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 = 7100 and estimated standard deviation σ = 2450. 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) 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.)
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! z=(x-mean)/sd
=(3500-7100)/2450=-3500/2450=-1.43
probability x<3500 is probability z<-1.43, which is 0.0764.
----------------------
For b, I get the same thing. I am not clear how this is different.
I am not certain what they mean by c.
If it is the probability that all 3 tests are <3500, it would be 0.0764^3, assuming independence, and that is 0.0004.
If it is the probability it happens at least once, then it is 1- probability it doesn't happen three times in a row, which is (1)-(0.9236)^3= 1-(0.7874)=0.2126.
|
|
|
