The state bridge design engineer has devised a plan to repair North Carolina\'s

Question

The state bridge design engineer has devised a plan to repair North Carolina's 4196 bridges that are currently listed as being in either poor or fair condition. The state has a total of 13,308 bridges. Before the governor will include the cost of this plan in his budget, he has decided to personally visit and inspect five bridges that are to be randomly selected.

(a) What is the probability that the governor will visit no bridges rated as poor or fair. (Give your answer correct to three decimal places.)


(b) What is the probability that the governor will visit one or two bridges rated as poor or fair. (Give your answer correct to three decimal places.)


(c) What is the probability that the governor will visit five bridges rated as poor or fair. (Give your answers correct to five decimal places.)

Explanation / Answer

Solution:-

x = 4196, N = 13308

p = 4196/13308

p = 0.3153

a) The probability that the governor will visit no bridges rated as poor or fair is 0.1505.

x = 0, n = 5

By applying binomial distribution:-

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

P(x = 0) = 0.1505.

b) The probability that the governor will visit one or two bridges rated as poor or fair is 0.6656.

x = 1 or 2, n = 5

By applying binomial distribution:-

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

P(x = 1 or 2) = P(x = 1) + P(x = 2)

P(x = 1 or 2) = 0.3465 + 0.3191

P(x = 1 or 2) = 0.6656

c) The probability that the governor will visit five bridges rated as poor or fair is 0.00312.

x = 5, n = 5

By applying binomial distribution:-

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

P(x = 5) = 0.00312

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