Question

Assume that 20% of all plants in a field are infested with aphids. Suppose that you pick 35 plants at random. What is the probability that none of them carried aphids? Determine the values of n, p, and k for the binomial distribution. n = p= k= (Type integers or decimals.)

Answer 1

Plants Infested with aphids = 20%

P(aplant isinfested with aphids) =0.20

Let X denote the number of infested plants with aphids in a pick of 35 plants.

Here X follows Binomial distribution with parameters

n= 35 (number of picks)

p=0.20 (probability of plant infested with aphids)

k=number of plants infested with aphids in the pick of 35 plants

Possible values of k are 0,1,2,...,35

$P(X=k)=\binom{35}{k}(0.20)^{k}(1-0.20)^{35-k},k=0,1,2...,35$

P(None of the plants carried aphids) = P(X = 0)

$P(X=0)=\binom{35}{0}(0.20)^{0}(1-0.20)^{35-0}=(0.80)^{35}$