1. If the population mean is 1,247, the population variance is 10,000, and the sample size is 100, what is the probability that X will be less than 1,230?
2. When sampling is from a population with standard deviation C = 55, using a sample of size n = 150, what is the probability that X will be at least 8 units away from the population mean µ,?
3. The Colosseum, once the most popular monument in Rome, dates from about AD 70. Since then, earthquakes have caused considerable damage to the huge structure, and engineers are currently trying to make sure the building will survive future shocks. The Colosseum can be divided into several thousand small sections. Suppose that the average section can withstand a quake measuring 3.4 on the Richter scale with a standard deviation of 1.5. A random sample of 100 sections is selected and tested for the maximum earthquake force they can withstand. What is the probability that the average section in the sample can withstand an earthquake measuring at least 3.6 on the Richter scale?