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?

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