Question

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Geometric distributions

Soundtronics is a company that manufactures inexpensive headphones at a high volume. Due to the high production rate, some of the headphones are defective when they come off of the production line. The probability that a set of headphones is defective is 0.39%. Find the probability that the first set of defective headphones is not one of the first 55 sets off of the production line.
A. 11%
B. 19%
C. 81%
D. 89%

Answer 1

Answer:

P(55 good before first defective) = 80.66%, so take choice C, 81%.

Step-by-step explanation:

We want probability of 55 or more successes before a failure.

P(success) = 1 - P(failure)

= 1.0000 - 0.0039 = 0.9961

We assume the outcomes are independent.

P(55 successes with no failure) = 0.9961^55 = 0.80660647769

Answer 2

Answer:

P(success) = 1 - P(failure)

?  =  1.0000 - 0.0039 = 0.9961

P(55 successes with no failure) = 0.9961^55 = 0.80660647769

the answer is C 81%  (we rounded)

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