Question

Of all the trees planted by a landscaping firm, 75% survive. What is the probability that 11 or more of the 13 trees they just planted will survive? (Use a table of binomial probabilities. Give your answer correct to four decimal places.)

Answer 1

Here, n = 13, p = 0.75, (1 - p) = 0.25 and x = 11
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X > =11).
P(X <= 10) = (13C0 * 0.75^0 * 0.25^13) + (13C1 * 0.75^1 * 0.25^12) + (13C2 * 0.75^2 * 0.25^11) + (13C3 * 0.75^3 * 0.25^10) + (13C4 * 0.75^4 * 0.25^9) + (13C5 * 0.75^5 * 0.25^8) + (13C6 * 0.75^6 * 0.25^7) + (13C7 * 0.75^7 * 0.25^6) + (13C8 * 0.75^8 * 0.25^5) + (13C9 * 0.75^9 * 0.25^4) + (13C10 * 0.75^10 * 0.25^3)
P(X <= 10) = 0 + 0 + 0 + 0.0001 + 0.0009 + 0.0047 + 0.0186 + 0.0559 + 0.1258 + 0.2097 + 0.2517
P(X <= 10) = 0.6674

P(X>=11) = 1- P(x< =10)
= 1- 0.6674

= 0.3326