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 48 cables and apply weights to each of them until they break. The 48 cables have a mean breaking weight of 776.5 lb. The standard deviation of the breaking weight for the sample is 16.1 lb. Find the 90% confidence interval to estimate the mean breaking weight for this type cable.