The tread-life of snow tires can be described by a normal model with a mean of 36,000 miles and a standard deviation of 2500 miles.
1. Could we expect our tire to last 42,000 miles? Explain using statistical reasoning and show all calculations, should include z-score and the probability.
2. Approximately ___________________ of tires will last between 30,000 miles and 40,000 miles. (to the nearest tenth of a percent)
3. The snow tire company wants to advertise 10% of their snow tires last longer than 45,000 miles. If the standard deviation remains at 2500 miles, what must the mean life-span of the tread be improved to? Show work.