find the probability

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. (Round your answer to four decimal places.)

Answer 1

X ~ Binomial(n = 25, p = 0.5)

n = 25 patients that called for medical advice

p = 0.5 (probability of a patient having a flu)

q = 1 - p = 0.5 (probability of a patient having a nasty cold)

₂₅

∑_k=5 C(25, k)*p^kq^n-k

This is the formula for the binomial cumulative density function. You should do this in the graphing calculator (TI-83, TI-84, or higher). Therefore, you will get

P(k ≥ 5) = 1 - P(k < 5) = 1 - 0.998 = 0.002

The probability that at least 5 patients who called for a medical advice have a flu is about 0.002.