Problem1

(a) If 100 people are interviewed for an opinion poll, what is the probability that the sample mean Sn/n differs in more than 10% from the true value p of the proportion of voters voting for candidate A? Report the figures given by both Chebyshev's inequality and by the the Central Limit Theorem. (b) Suppose now that you want to have 95% confidence that S_n/n differs from the true value p in no more than 1%. How many voters should be sampled? Report the figures given by both Chebyshev's inequality and by the Central Limit Theorem.

Problem2

(a) Four identical bulbs with average lifetime 1,000 hours are turned on simultaneously. What is the expected value of the time needed, starting at the moment they were turned on, for all of them to burn?

(b) (2 POINTS) Now we turn one of the bulbs and wait until it burns, and at that moment we turn on a second bulb and wait until it burns and do the same thing for the two remaining bulbs. What is the expected value of the time needed, starting at the moment the first one was turned on, for all of them to burn?

(c) (3 POINTS) Use the normal approximation to approximate the probability that the time in part (b) exceeds 5,000 hours.

PLEASE TYPE YOUR ANSWER!!!