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Statistics Question poisson distribution?

#10405

The probability that a student fails the screening test for scoliosis (curvature of the spine) at a local high school is known to be 0.004. Of the next 1875 students who are screened for scoliosis, find the probability that

A. fewer than 5 fail the test?

B. 8, 9, or 10 fail the test

#10406

Use the formula
P(x = r) = nCr p^r q^(n-r)

where n is the number of times an event has occurred, p is the probability of occurrence of a particular event, q is 1-p and r is the number of times the required events happen.

Here n=1875, p = 0.004, q = 0.996

A. Find P(x = 0) + P(x =1) + P(x=2) + P(x=3) + P(x=4)

B. Find P(x = 8) + P(x = 9) + P(x = 10)

#10407

solving with the above formula (given by Alex) we get,
A) P(x = 0) + P(x =1) + P(x=2) + P(x=3) + P(x=4) = 0.13155
b) P(x = 8) + P(x = 9) + P(x = 10) = 0.33817

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