Question

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?

Answer 1

Number of diodes expected to fail = 2

Standard deviation of those that will fail = 1.41

Step-by-step 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