Find the indicated probabilities.
1. A random sample of size n = 100 is obtained from a population with µ = 1200 and σ = 250. Find the probability that the sample mean will lie between 1200 and 1250.
2. IQ scores for adults are normally distributed, with mean µ = 100 and standard deviation σ = 15. If a random sample of 16 adults is selected, find the probability that the average IQ score in the sample will be at least 92.5.