A survey found 10% of problems in school were caused by violent actions of students. If a randomly selected sample of 10 school problems were selected, find the probability that more than 2 were caused by violent actions.

Answer:

The Probability of success $ (p) = 0.10 $

The Sample size $ (n) = 10 $

Solution:

The probability that more than 2 were caused by violent actions:

$P(x > 2) = 1 – P(x \leq 2)$

$P(x > 2) = 1 – \Sigma_{x=0}^{2} (nCx) * p^x * (1 – p)^{n – x}$

$P(x > 2) = 1 – \Sigma_{x=0}^{2} (10Cx) * 0.10^x * (1 – 0.10)^{10 – x}$

$P(x > 2) = 1 – 0.9298$

$P(x > 2) = 0.0702$

Final Answer:

The probability that more than 2 were caused by violent actions $=0.0702 $

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