A population has a mean of 110.22 and a standard deviation of 5.68. For which sample size does 95% of the sample means fall within the interval between 109.08 and 111.36?

You are standing next to a really big circular lake. you want to measure the diameter of the lake, but you don't want to have to swim across with a measuring tape! you decide to walk around the perimeter of the lake and measure its circumference, and find that it's 400\pi\text{ m}400? m. what is the diameter dd of the lake?