Question

The resistances produced by a manufacturer follow a normal distribution with a mean of 150 ohm and standard deviation = 5ohm What percentage of resistors will have a resistance between 140ohm and 160ohm?

Answer 1

<img src="/cgi-bin/mimetex.cgi?z_%7B1,2%7D%20=%20%5Cpm%5Cfrac%7B150-140%7D%7B5%7D%20=%5Cpm2%5C%5C%20P%28140%3CX%3C160%29=2%20p%28z=2%29=%202*%200.477%20=%200.954%20=%2095.4%20%5C%" title="z_{1,2} = \pm\frac{150-140}{5} =\pm2\\ P(140<X<160)=2 p(z=2)= 2* 0.477 = 0.954 = 95.4 \%">