Question

9. People who have been in contact with a carrier of a disease, have a 40% chance of contracting the disease. Suppose that the carrier of the diseases may have infected a school with 500 people. Find the approximate probability that at least 215 people will contract the disease.

A. 0.09

B. 0.91

C. 0.05

D. 0.89

Answer 1

Solution:

We are given n = 500, p = 0.40, q = 1 – p = 1 – 0.40 = 0.60

Mean = np = 500*0.40 = 200

SD = sqrt(npq) = ssqrt(500*0.40*0.60) = 10.95445

We have to find P(X≥215) = P(X>214.5) by using continuity correction.

P(X>214.5) = 1 – P(X<214.5)

Z = (X – mean)/SD

Z = (214.5 – 200)/ 10.95445

Z = 1.323663

P(Z<1.323663) = P(X<214.5) = 0.907192

P(X>214.5) = 1 – P(X<214.5)

P(X>214.5) = 1 – 0.907192

P(X>214.5) = 0.092808

P(X>214.5) = 0.09

Correct Answer: A. 0.09