2. 20 traffic lights were installed in Newark. The probability that a bullb fail

Question

2. 20 traffic lights were installed in Newark. The probability that a bullb fails within 10,000 hours of operation is 0.35. Assume that each bullb fails independently (a) What is the probability that fewer than 4 (four) of the original bulbs fail within 10,000 hours? (b) What is the probability that none of the original bulbs fail withirn 10,000 hours? (c) What is the probability that more than 5 (ive) of the original bulbs fail within 10,000 hours? (d) What is the expected number of bulbs surviving 10,000 hours of operation? What is the standard deviation? Show all your work. Total = 10 pts.

Explanation / Answer

Answer to the question is given below. Please write back in case you don't understand any part of it :

20.

a. This is given by :

P(X<4) = 20C0 (.35^0)(.65^20) + 20C1 (.35^1)(.65^19) +20C2 (.35^2)(.65^18) +20C3 (.35^3)(.65^17)

= 0.04438

b. P(none of them fail) = 20C0 (.35^0)(.65^20) = =0.0002

c. P(X>5) = 1 - P(X<=4) = 1- (20C0 (.35^0)(.65^20) + 20C1 (.35^1)(.65^19) +20C2 (.35^2)(.65^18) +20C3 (.35^3)(.65^17) +20C4 (.35^4)(.65^16))

=0.7546

d. Expected value = np = 20*.35 = 7

Standard deviation = sqrt(npq) = sqrt( 20*.35*.65) = 2.1331

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