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 = 6400 and estimated standard deviation σ = 2050. 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 = 6400 and σx = 1449.57. The probability distribution of x is not normal. The probability distribution of x is approximately normal with μx = 6400 and σx = 1025.00. The probability distribution of x is approximately normal with μx = 6400 and σx = 2050. 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 stayed the same as n increased. 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? 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 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 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 does not have leukopenia.
a)
probability that, on a single test, x is less than 3500 :
| probability = | P(X<3500) | = | P(Z<-1.41)= | 0.0793 |
b)
The probability distribution of x is approximately normal with μx = 6400 and σx = 1449.57.
| probability = | P(X<3500) | = | P(Z<-2)= | 0.0228 |
c)
| sample size =n= | 3 |
| std error=σx̅=σ/√n= | 1183.5681 |
| probability = | P(X<3500) | = | P(Z<-2.45)= | 0.0071 |
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.
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