Question: A manufacturer claims that the life of a gun barrel on their standard-issue Glock is 2,540 shots. A random sample of 100 guns is collected, and it is found that the average lifespan of their barrels is 2,524 shots with a standard deviation of 93 shots. Does the population mean for the gun barrels fall within the 98% confidence level of this sample? Explain your reasoning using words and/or a diagram.