Question

Use the following information to answer the next three exercises. 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. (a) Define the random variable X and state its distribution. (b) On average, for every 25 patients calling in, how many do you expect to have the flu? (c) Find the probability that at least four of the 25 patients actually have the flu.

Answer 1

p = 0.04

n = 25

a) X represents the number of patients having the flu out of 25.

This is a binomial distribution.

n = 25

p = 0.04

P(X = x) = 25Cx * 0.04^x * (1 - 0. 04)^25-x

b) Expected value = n * p = 25 * 0.04 = 1

c) P(X > 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3))

                  = 1 - (25C0 * 0.04⁰ * 0.96²⁵ + 25C1 * 0.04¹ * 0.96²⁴ + 25C2 * 0.04² * 0.96²³ + 25C3 * 0.04³ * 0.96²²)

                  = 1 - 0.9835

                  = 0.0165