A certain insecticide kills 80% 80% of all insects in laboratory experiments. A sample of 14 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 2 insects will survive? Round your answer to four decimal places.

The probability that exactly 2 insects will survive = 0.2501

Step-by-step explanation:

Given: A certain insecticide kills 80% of all insects in laboratory experiments.

The probability that a particular insect survives= 1-0.80=0.20

Sample size: n=14

Binomial probability distribution:

, where x= number of successes , p=probability of success in each trial, n= sample size.

The probability that exactly 2 insects will survive =

Hence, the probability that exactly 2 insects will survive = 0.2501