Question

Question 11 Traffic engineers install 8 street lights with new bulbs. The probability that a bulb will fail within 50010 hours of operation is 0.18. Assume that each of the bulbs fails independently. (a) What is the probability that fewer than two of the original bulbs will fail within 50010 hours of operation? (b) What is the probability that no bulbs will have to be replaced within 50010 hours of operation? (c) What is the probability that more than four of the original bulbs will need replacing within 50010 hours? Your answer should be correct to 3 decimal places. Your answer should be correct to 3 decimal places. Your answer should be correct to 6 decimal places.

Answer 1

This is a binomial distribution with parameters:

n = 8, p = 0.18

Hence,

a) P(Fewer than two)

= P(X < 1)

= binom.dist(1, 8, 0.18, True) [Excel Formula]

= 0.563

b) P(No bulb)

= P(X = 0)

= (1 - 0.18)⁸

= 0.204

c) P(More than 4)

= 1 - P(X < 4)

= 1 - binom.dist(4, 8, 0.18, True)    [Excel Fromula]

= 0.006516