8.10 Resistors of a certain type have resistances that average 200 ohms, with a standard deviation of 10 ohms. Twenty-five of these resistors are to be used in a circuit.

a Find the probability that the average resistance of the 25 resistors is between 199 and 202 ohms.

b Find the probability that the total resistance of the 25 resistors does not exceed 5,100 ohms.

[Hint: Note that

.]

c What assumptions are necessary for the answers in parts

(a) and

(b) to be good approximations?