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Research has shown the 30% of all houses ( p = 0.3) have faulty wiring. An...

Research has shown the 30% of all houses ( p = 0.3) have faulty wiring. An inspection was done of 18 houses.

Find the probability that four (4) houses have faulty wiring.

Probability that at least 1 house has faulty wiring.

Find the mean and standard deviation.

Math   Statistics-And-Probability   
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Answer #1

Let X denotes the number of houses that have faulty wiring in a random sample of 18 houses.

X ~ Binomial(n = 18, p = 0.3)

The probability mass function of X is

Now,

The probability that four (4) houses have faulty wiring

The probability that at least 1 house has faulty wiring

The mean is E(X) = n*p = 18*0.3 = 5.4

The standard deviation is

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