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17 December, 06:01

In proof testing of circuit boards, the probability that any particular diode will fail is 0.01. Suppose a circuit board contains 200 diodes, all which are independent of one another. A board works properly only if all its diodes work. How many diodes would you expect to fail, and what is the standard deviation of the number that will fail?

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  1. 17 December, 06:30
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    Number of diodes expected to fail = 2

    Standard deviation of those that will fail = 1.41

    Explanation:

    The number of diodes failing is a binomial random variable with n = 200 and p = 0.01

    And so, E (X) = n * p = 200 * 0.01 = 2

    The variance of this binomial random variable is given as

    n * p * (1 - p) = 200 * 0.01 * 0.99 = 1.98

    But, standard deviation is

    √ (v) = √ (1.98) = 1.41
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