Question

Suppose that the probability a lost microchipped dog is returned to its owner is 0.53. What is the probability that in a sample of 30 lost microchipped dogs that less than 12 will be returned to their owner?

		0.946
		0.054
		0.893
		0.107

Answer 1

Here, n = 30, p = 0.53, (1 - p) = 0.47 and x = 12
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X <= 11).
P(X < 12) = (30C0 * 0.53^0 * 0.47^30) + (30C1 * 0.53^1 * 0.47^29) + (30C2 * 0.53^2 * 0.47^28) + (30C3 * 0.53^3 * 0.47^27) + (30C4 * 0.53^4 * 0.47^26) + (30C5 * 0.53^5 * 0.47^25) + (30C6 * 0.53^6 * 0.47^24) + (30C7 * 0.53^7 * 0.47^23) + (30C8 * 0.53^8 * 0.47^22) + (30C9 * 0.53^9 * 0.47^21) + (30C10 * 0.53^10 * 0.47^20) + (30C11 * 0.53^11* 0.47^19)
P(X < 12 ) = 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0.001 + 0.002 + 0.006 + 0.015 + 0.030
P(X < 12 ) = 0.054