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A “blood count” is a widely-used laboratory test. The test consists of (1) a count of...

A “blood count” is a widely-used laboratory test. The test consists of (1) a count of the total number of white blood cells in a blood sample and (2) how many lymphocytes, neutrophils, monocytes, eosinophils and basophils are present in the sample. The probability of being a neutrophil is 0.06. Assuming a binomial probabilistic model for the number of neutrophils, determine:

a) What is the probability that 4 out of 100 white blood cells in the sample are neutrophils? 


b) What is the probability that 50 out 100 white blood cells in the sample are neutrophils? 


c) What is the probability that the number of neutrophils in 100 white blood cells is at most 4 (≤ 4)?

d) What is the probability that the number of neutrophils in 100 white blood cells is > 4?

e) What conditions need to be meet for a binomial model to apply? 


math   Statistics-And-Probability   
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Answer #1

Let X denote the number of white blood cells in the sample that are neutrophils. Then

a)

Required probability =

b)

Required probability =

c)

Required probability =

d)

Required probability =

e)

The conditions that need to be met are:

1) The number of trials should be finite.

2) The trials should be independent of each other.

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