Solution:
Let X be a random variable which represents the number of insects survive in the laboratory experiment.
A certain insecticide kills 80% of all insects. It means 20% of the all insecticide survive.
Probability that an insect survive = 20/100 = 0.20
Let us consider survival of insects as success.
Hence, probability of success (p) = 0.2
Number of trials (n) = 14
Since, probability of success remains constant throughout the experiment, number of trials (n) is finite, there are only two outcomes of an trial (success and failure), therefore we can consider that X is binomial distributed random variable.
According to binomial probability law,
Probability of occurrence of exactly x successes in n trials is given by,
; x = 0, 1, 2, ..............., n
We have to obtain P(X > 5). And we have n = 14 and p = 0.20
Using binomial probability law we get,
[Since, n! = n(n-1)(n-2)(n-3)! , 2! = (2×1)=2, 3! = (3×2×1)=6, 4! = (4×3×2×1)=24 and 5! = (5×4×3×2×1)=120]
Probability that more than 5 insects will survive is 0.0439.
A certain insecticide kills 80% of all insects in laboratory experiments. A sample of 14 insects...
A certain insecticide kills 70% 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 3 insects will survive? Round your answer to four decimal places.
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