Experiments on 100 batteries have been conducted to estimate the battery life of an electric vehicle. From the results, the average life of a battery is found to be 1300 cycles with a standard deviation of 100 cycles. 500,000 electric cars equipped with this battery type have been sold and are running on the road. Determine:
1. After how many cycles will 5% of the batteries' life end?
2. How many batteries are expected to have a life between 1450 and 1500 cycles?
3. How many batteries are expected to have a life less than 1100 cycles?
4. What assumptions must one make to determine the above-mentioned parameters?