An insurer knows that 2 out of every 10 people who hire its services do so for more than one insurance. Find the probability that, in the next 40 contracts, between 7 and 12 clients purchase more than one insurance. * You must associate the resolution of the exercise with a discrete distribution function.

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Answer to a math question An insurer knows that 2 out of every 10 people who hire its services do so for more than one insurance. Find the probability that, in the next 40 contracts, between 7 and 12 clients purchase more than one insurance. * You must associate the resolution of the exercise with a discrete distribution function.

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103 Answers

X \sim Binomial(n = 40, p = 0.2)

P(7 \leq X \leq 12) = P(X \leq 12) - P(X \leq 6)

P(X \leq 12) = \sum_{k=0}^{12} \binom{40}{k} (0.2)^k (0.8)^{40-k}

P(X \leq 6) = \sum_{k=0}^{6} \binom{40}{k} (0.2)^k (0.8)^{40-k}

Plugging these values into the sum functions or using statistical software, we find:

P(X\leq12)\approx0.9568

P(X\leq6)\approx0.2859

P(7\leq X\leq12)\approx0.9568-0.2859=0.6709

Answer:

P(7\leq X\leq12)\approx0.6709

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