Answer to Question #214431 in Statistics and Probability for EHSAN

Question

a)     Wires manufactured for a certain computer system are specified to have a resistance of between 0.11 and 0.16 ohm. The actual measured resistances of the wires produced by Company A have a normal probability distribution, with a mean of 0.14 ohms, and a standard deviation of 0.003 ohms. What is the probability that a randomly selected wire from Company A’s production lot will meet the specifications?

Answer 1

Let $X=$ resistances of the wire: $X\sim N(\mu, \sigma^2).$

Given $\mu=0.14\ ohms, \sigma=0.003\ ohms.$

$$P(0.11<X<0.16)=P(X<0.16)-P(X\leq0.11)$$

$$=P(Z<\dfrac{0.16-0.14}{0.003})-P(Z\leq \dfrac{0.11-0.14}{0.003})$$

$$\approx P(Z<6.6667)-P(Z\leq -10)$$

$$\approx1$$