Question

When treated with an​ antibiotic, 94​% of all the dolphins are cured of an ear infection. If 8 dolphins are​ treated, find the probability that exactly 4 are cured.

Answer 1

Answer:

0.071%

Step-by-step explanation:

The probability of success is constant, and each dolphin is independent, so this is an example of a binomial distribution.

P = nCr p^r q^(n-r)

where P is the probability of r number of successes out of n number of trials, p is the probability of success, and q is probability of failure (1-p).

Given: n = 8, r = 4, p = 0.94, q = 0.06:

P = ₈C₄ (0.94)⁴ (0.06)⁸⁻⁴

P = 70 (0.94)⁴ (0.06)⁴

P ≈ 0.071%