Question: A company assembles a large part by joining two smaller parts together. Assume that the smaller parts are normally distributed with a mean length of 1 inch and a standard deviation of 0.01 inch.
a. What fraction of the larger parts are longer than 2.05 inches? (Use the fact that the sum of independent normal random variables is normally distributed, with mean equal to the sum of the individual means and variance equal to the sum of the individual variances.)
b. What fraction of the larger parts are between 1.96 inches and 2.02 inches long?