Question

For a binomial probability function with P=0.6 and n=16​, find the probability that the number of successes is equal to 9 and the probability that the number of successes is fewer than 7.

Answer 1

Here, n = 16, p = 0.6, (1 - p) = 0.4 and x = 9
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 9)
P(X = 9) = 16C9 * 0.6^9 * 0.4^7
P(X = 9) = 0.1889
0

Here, n = 16, p = 0.6, (1 - p) = 0.4 and x = 7
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X < 7).
P(X < 7) = (16C0 * 0.6^0 * 0.4^16) + (16C1 * 0.6^1 * 0.4^15) + (16C2 * 0.6^2 * 0.4^14) + (16C3 * 0.6^3 * 0.4^13) + (16C4 * 0.6^4 * 0.4^12) + (16C5 * 0.6^5 * 0.4^11) + (16C6 * 0.6^6 * 0.4^10)
P(X < 7) = 0 + 0 + 0.0001 + 0.0008 + 0.004 + 0.0142 + 0.0392
P(X < 7) = 0.0583