Use computer Assume that X is a hypergeometric random variab

(Use computer) Assume that X is a hypergeometric random variable with N = 40, S = 19, and n = 9. Calculate the following probabilities. (Round your answers to 4 decimal places.)

Solution

Using technology like Excel, you can use the function

=HYPGEOM.DIST(x, n, S, N, cumulative)

cumulative = 0 if you want exactly x successes

cumulative = 1 if you want at most x successes

a)

P(x = 4) can be obtained by typing

=HYPGEOM.DIST(4,9,19,40,0)

=0.288447363 [ANSWER]

b)

Note that

P(at least 2) = 1 - P(at most 1)

Thus, we can type

=1 - HYPGEOM.DIST(1,9,19,40,1)

= 0.984785485 [answer]

c)

We can type

=HYPGEOM.DIST(6,9,19,40,1)

to get

P(at most 6) = 0.955159705 [answer]