Question

In a production line, 1000 Ω resistors with 10% tolerance are produced. Resistance value X is the gauss random variable with an expected value of 1000 and 2500 variations. Find the probability that a randomly selected resistance will be outside acceptable limits.

Answer 1

Let, define a random variable X that represent resistance of resistors.

The random variable X is normally distributed with mean 1000 and variance 2500.

Here, the resistors with 10% tolerance are produced.

So, the acceptable region is

Find the probability that a randomly selected resistance will be outside acceptable limits.

i.e, P(resistance outside acceptable limits)

The probability is 0.0455003