Question

Assume that World Health Organization declares that there is a 25 percent chance that a virus that caused a recent pandemic can infect anyone. Assume that you sampled 8 people. a. What is the probability that this virus will infect at least four people? b. What is the standard deviation of the number of infected people? c. What is the probability that this virus will infect three people? d. Assume that you have a friend who told you that this virus is not infectious and no one in this sampled group should be infected. Do you think he is right? Explain using probabilities.

Answer 1

X ~ Bin ( n, p)

Where n = 8 , p = 0.25

Binomial probability distribution is

P(X) = nCx * px ( 1 - p)n-x

a)

P(X >= 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)

= 8C4 *0.254 * ( 1 - 0.25)4 + 8C5 *0.255 * ( 1 - 0.25)3 + 8C6 *0.256 * ( 1 - 0.25)2 + 8C7 *0.257 * ( 1 - 0.25)1 +

8C8 *0.258 * ( 1 - 0.25)0

= 0.1138

b)

Standard deviation = sqrt [ n p ( 1 - p) ] = sqrt [ 8 * 0.25 ( 1 - 0.25) ] = 1.2247

c)

P(X = 3) = 8C3 *0.253 * ( 1 - 0.25)5

= 0.2076

d)

P(X = 0) = 8C0 *0.250 * ( 1 - 0.25)8

= 0.1001

Since probability is greate than 0.05, the event is usual.

Yes, he is right