3. A production line manufactures 1000 ohms resistors that must satisfy a 10% tolerance.
a. If a resistance is adequately described by a Gaussian random variable for which mean = 1000; and standard deviation = 40;, what fraction of the resistance expected to be rejected?
b. If a machine is not properly adjusted, the product resistances changes, the case where mean= 1050; (5% shift). What fraction is now rejected?
4. At a certain military installation six similar radars are placed in operation. It is known that radar's probability of failing to operate before 500 hours of "on" time have accumulated is 0.06. What are the probabilities that, before 500 hours have elapsed, (a) all will operate, (b) all will fail, and (c) only one will fail?