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 = 6900 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) 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 μx = 6900 and σx = 2450. The probability distribution of x is approximately normal with μx = 6900 and σx = 1732.41. The probability distribution of x is approximately normal with μx = 6900 and σx = 1225.00. 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?
The probabilities increased as n increased.
The probabilities decreased as n increased.
The probabilities stayed the same 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 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.
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.
a)
| for normal distribution z score =(X-μ)/σ | |
| here mean= μ= | 6900 |
| std deviation =σ= | 2450.000 |
probability that, on a single test, x is less than 3500:
| probability = | P(X<3500) | = | P(Z<-1.39)= | 0.0823 |
b)
The probability distribution of x is approximately normal with μx = 6900 and σx = 1732.41.
probability of x < 3500
| probability = | P(X<3500) | = | P(Z<-1.96)= | 0.0250 |
c)
| sample size =n= | 3 | |||
| std error=σx̅=σ/√n= | 1414.5082 | |||
| probability = | P(X<3500) | = | P(Z<-2.4)= | 0.0082 |
d)
The probabilities decreased as n increased.
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.
Get Answers For Free
Most questions answered within 1 hours.