1. A manufacturer of car batteries claims that the life of their batteries is normally distributed with mean µ = 58 months and standard deviation σ = 3. Determine the probability that a randomly selected battery will last at least 62 months.
2. Assume that the income of pediatricians is normally distributed with mean µ = $100,000 and standard deviation σ = 10,000. Determine the probability of observing an income between $85,000 and $115,000.