A manufacturer knows from his experience that the resistance of resistors he produces is Normal with μ=100 ohms & standard deviation σ=20 ohms.

Subject: Applied Mathematics 4

Topic: Probability

Difficulty: Medium

The standard normal variate X is given by:

$ Z = \frac{X - \mu}{\sigma} = \frac{X - 100}{20} $

P(98 $\leq$ X $\leq$ 102).

When X = 98, $ Z = \frac{98 - 100}{20} = \frac{-2}{20} = -0.1 $

When X = 102 $ Z = \frac{102 - 100}{20} = \frac{2}{20} = 0.1 $

P(98 $\leq$ X $\leq$ 102) = P(-0.1 $\leq$ Z $\leq$ 0.1)

= 2 x P(0 $\leq$ Z $\leq$ 0.1)

= 2(0.0398) = 0.0796

% of resistors having resistance between 98 and 102 ohms = 100 x 0.0796 = 7.96 = 8%