A group of engineers developed a new design for a steel cable. They need to estimate the amount of weight the cable can hold. The weight limit will be reported on cable packaging. The engineers take a random sample of 50 cables and apply weights to each of them until they break. The 50 cables have a mean breaking weight of 774.6 lb. The standard deviation of the breaking weight for the sample is 15.1 lb.

Find the 99% confidence interval to estimate the mean breaking weight for this type cable.