Question

A local veterinary clinic typically sees 15% of its horses presenting with West Nile virus. If 10 horses are admitted during July, what is the probability that two or fewer horses among the 10 horses admitted have been infected with West Nile virus?
A. 0.3874
B. 0.3487
C. 0.1937
D. 0.8202

Answer 1

Answer: D. 0.8202

Step-by-step explanation:

We would assume a binomial distribution for the number of horses presenting with West Nile virus. The formula is expressed as

P(x = r) = nCr × p^r × q^(n - r)

Where

x represent the number of successes.

p represents the probability of success.

q = (1 - p) represents the probability of failure.

n represents the number of trials or sample.

From the information given,

p = 15% = 15/100 = 0.15

q = 1 - p = 1 - 0.15

q = 0.85

n = 10

Therefore,

P(x ≤ 2) = P(x = 0) + P(x = 1) + P(x = 2)

P(x = 0) = 10C0 × 0.15^0 × 0.85^(10 - 0) = 0.1969

P(x = 1) = 10C1 × 0.15^1 × 0.85^(10 - 1) = 0.3474

P(x = 2) = 10C2 × 0.15^2 × 0.85^(10 - 2) = 0.2759

P(x ≤ 2) = 0.1969 + 0.3474 + 0.2759

= 0.8202