Question

A new variety of turf grass developed for use on golf courses is claimed to have a germination rate of 85%. To evaluate this claim, 100 seeds are randomly selected and planted in a greenhouse so that they are exposed to identical conditions. If the germination rate is 85% as claimed. What represents the approximate probability that 92 seeds or more will germinate?

Answer 1

Probability = 0.01531

Explanation:

Prob (Getting 92 out of 100 germinated seeds) follows binomial probability distribution.

N = Number of seeds = 100. r = Number of success (germination) = 92

r = No. Success = Seed germination, Prob (Success) ie P = 85% = 0.85 , Prob (non success ie non germination) ie Q = 1 - 85% = 15% = 0.15

Probability = N c r . (P)^r . (Q)^(n-r)

= 100c92 (0.85)^92 (0.15)^8

= 186087894300 (0.000000321026708) (0.000000256289062)

= 0.01531 {Approx}