Traffic engineers install 7 street lights with new bulbs. The probability that a
ID: 3130108 • Letter: T
Question
Traffic engineers install 7 street lights with new bulbs. The probability that a bulb will fail within 50040 hours of operation is 0.15. Assume that each of the bulbs fails independently.
(a) What is the probability that fewer than two of the original bulbs will fail within 50040 hours of operation?
(b) What is the probability that no bulbs will have to be replaced within 50040 hours of operation?
(c) What is the probability that more than four of the original bulbs will need replacing within 50040 hours?
Explanation / Answer
a)
Note that P(fewer than x) = P(at most x - 1).
Using a cumulative binomial distribution table or technology, matching
n = number of trials = 7
p = the probability of a success = 0.15
x = our critical value of successes = 2
Then the cumulative probability of P(at most x - 1) from a table/technology is
P(at most 1 ) = 0.71658408
Which is also
P(fewer than 2 ) = 0.71658408 [ANSWER]
********************
b)
Note that the probability of x successes out of n trials is
P(n, x) = nCx p^x (1 - p)^(n - x)
where
n = number of trials = 7
p = the probability of a success = 0.15
x = the number of successes = 0
Thus, the probability is
P ( 0 ) = 0.320577088 [ANSWER]
*******************
c)
Note that P(more than x) = 1 - P(at most x).
Using a cumulative binomial distribution table or technology, matching
n = number of trials = 7
p = the probability of a success = 0.15
x = our critical value of successes = 4
Then the cumulative probability of P(at most x) from a table/technology is
P(at most 4 ) = 0.998778355
Thus, the probability of at least 5 successes is
P(more than 4 ) = 0.001221645 [ANSWER]
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.