1. From a large collection of bolts which is known to contain 3% defec- tive bolts, 1,000 are chosen at random. If X is the number of the defective bolts among those chosen, what is probability that this number does not exceed 5% of 1,000? (Use the CLT.)
2. Suppose that 53% of the voters favor a certain legislative proposal. How many voters must be sampled, so that the observed relative frequency of those favoring the proposal will not differ from the assumed frequency by more than 2% with probability 0.99? (Use the CLT.)