Question

A certain insecticide kills 60% of all insects in laboratory experiments. A sample of 12 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 10 insects will die

Answer 1

Answer:

The probability that exactly 10 insects will die

                     P( X = 10 ) = 0.06385        

Step-by-step explanation:

Step(i):-

Given a certain insecticide kills 60% of all insects in laboratory experiments

Given proportion  p = 0.60

                           q = 1 - 0.60 = 0.40

Given sample size 'n' = 12

Step(ii):-

Let "X' be the random variable of binomial distribution

                              $P(X=r) = n_{C_{r} } p^{r} q^{n-r}$

The probability that exactly 10 insects will die

                              $P(X=10) = 12_{C_{10} } (0.60)^{10} (0.40)^{12-10}$

                           

                          $n_{C_{r} } = \frac{n!}{(n-r)!r!} = \frac{12!}{(12-10)!10!} = 66$

                          $P(X=10) = 66 X (0.60)^{10} (0.40)^{2} = 0.06385$

Final answer:-

The probability that exactly 10 insects will die

                     P( X = 10 ) = 0.06385