Question

In: Statistics and Probability

At 25oC, 20% of a certain type of laser diodes have efficiency below 0.3 mW/mA. For...

At 25oC, 20% of a certain type of laser diodes have efficiency below 0.3 mW/mA. For five diodes, selected by simple random sampling from a large population of such diodes, find the probability of the following events.
(a) All five have efficiency above 0.3 at 25oC.
(b) Only the second diode selected has efficiency below 0.3 at 25oC. (c) Exactly one of the five diodes has efficiency below 0.3 at 25oC.

(d) Exactly two of the five diodes have efficiency below 0.3 at 25oC.

Solutions

Expert Solution

The probability that a randomly selected laser diode has efficiency below 0.3 mW/mA at is 0.20

Let X be the number of diodes out of randomly selected 5 diodes that have efficiency above 0.3 at .

We can say that X has a Binomial distribution with parameters, number of trails (number of diodes selected) n=5 and the success probability (probability that a randomly selected laser diode has efficiency below 0.3 mW/mA at ) p=0.20

The probability that X=x diodes out of 5 have efficiency above 0.3 at is given by the Binomial probability

a) The probability that all five have efficiency above 0.3 at 25oC is same as the probability that X=5 have efficiency above 0.3 at 25oC

ans: The probability that all five have efficiency above 0.3 at 25oC is 0.0003

b) The probability that only the second diode selected has efficiency below 0.3 at 25oC is (This is not a Binomial probability)

ans: The probability that only the second diode selected has efficiency below 0.3 at 25oC is 0.0819

c) The probability that exactly one of the five diodes has efficiency below 0.3 at 25oC is same as the probability that X=1 have efficiency above 0.3 at 25oC

ans: The probability that exactly one of the five diodes has efficiency below 0.3 at 25oC is 0.4096

d)The probability that exactly two of the five diodes has efficiency below 0.3 at 25oC is same as the probability that X=2 have efficiency above 0.3 at 25oC

ans: The probability that exactly two of the five diodes has efficiency below 0.3 at 25oC is 0.2048


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