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Sagot :
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
[tex]P(X=r) = n_{C_{r} } p^{r} q^{n-r}[/tex]
The probability that exactly 10 insects will die
[tex]P(X=10) = 12_{C_{10} } (0.60)^{10} (0.40)^{12-10}[/tex]
[tex]n_{C_{r} } = \frac{n!}{(n-r)!r!} = \frac{12!}{(12-10)!10!} = 66[/tex]
[tex]P(X=10) = 66 X (0.60)^{10} (0.40)^{2} = 0.06385[/tex]
Final answer:-
The probability that exactly 10 insects will die
P( X = 10 ) = 0.06385
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