Question

Recently, a nurse commented that when a patient calls the medical advice line claiming to have the flu, the chance that he or she truly has the flu (and not just a nasty cold) is only about 4%. Of the next 25 patients calling in claiming to have the flu, we are interested in how many actually have the flu.

Find the probability that at least five of the 25 patients actually have the flu.

Answer 1

X ~ B ( n = 25 , P = 0.04 )

P(X = 0 ) = 0.3604
P(X = 1 ) = 0.3754
P(X = 2 ) = 0.1877
P(X = 3 ) = 0.06
P(X = 4 ) = 0.0137

P ( X >= 5 ) = 1 - P ( X <= 4 ) = 1 - 0.9972 = 0.0028