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2 years ago

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A certain insecticide kills 60% of all insects in laboratory experiments. A sample of 12 insects is exposed to the insecticide i

n a particular experiment. What is the probability that exactly 10 insects will die

1 answer:

Vilka [71]2 years ago

4 0

Answer:

The probability that exactly 10 insects will die

P( X = 10 ) = 0.06385

Step-by-step explanation:

<u><em>Step(i):-</em></u>

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

<u><em>Step(ii):</em></u>-

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

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

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

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

<u><em>Final answer:</em></u>-

The probability that exactly 10 insects will die

P( X = 10 ) = 0.06385

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