I need some help solving these problems. Thank you! Let x be a random variable t
ID: 3220184 • Letter: I
Question
I need some help solving these problems. Thank you!
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 = 7200 and estimated standard deviation = 2550. 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? (Multiple Choice)
A. The probability distribution of x is approximately normal with x = 7200 and x = 1803.12.
B. The probability distribution of x is approximately normal with x = 7200 and x = 1275.00.
C. The probability distribution of x is approximately normal with x = 7200 and x = 2550.
D. The probability distribution of x is not normal.
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? (Multiple Choice)
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? (Multiple Choice)
A. 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.
B. 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.
C. 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.
D. 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.
Explanation / Answer
a) P(X<3500) =P(Z<(3500-7200)/2550)=P(Z<-1.4510)=0.0734
b)as std error =std deviation/(n)1/2
A. The probability distribution of x is approximately normal with x = 7200 and x = 1803.12.
P(X<3500)=P(Z<(3500-7200)/1803.12)=P(Z<-2.052)=0.0201
c)
The probability distribution of x is approximately normal with x = 7200 and x = 1472.243
P(X<3500)=P(Z<(3500-7200)/1472.243)=P(Z<-2.5132)=0.0060
d)C. The probabilities decreased as n increased.
D. 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.