Thirty percent f all automobiles undergoing an emissions inspection at a certain

Question

Thirty percent f all automobiles undergoing an emissions inspection at a certain inspection station fail the inspection. (Round all answers to three decimal places.) (a) (5 points) Among 15 randomly selected cars, what is the probability that at most 2 fail the inspection? (b) (5 points) Among 15 randomly selected cars, what is the probability that at least 3 fail the inspection'? (c) (5 points) Among 25 randomly selected cars, what is the mean value of the number that pass inspection, and what is the standard deviation of the number that pass inspection? (d) (5 points) What values of this random variable are within 1 standard deviation of the mean value?

Explanation / Answer

Solution:-

a) The probability that atmost 2 fail the inspection is 0.1268.

p = 0.30

x = 2

By applying binomial distribution

P(x,n) = nCx*px*(1-p)(n-x)

P(x < 2) = 0.1268

b)  The probability that atleast 3 fail the inspection is 0.8732.

p = 0.30

x = 3

By applying binomial distribution

P(x,n) = nCx*px*(1-p)(n-x)

P(x > 3) = 0.8732

c) The mean and standard deviation are

= n × p

= 25 × 0.30

= 7.5

= sqrt(n×p(1-p))

= 2.291

d) The value of this random variable are within 1 standard deviation of the mean value is 5.21. and 9.79.

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