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 45 cables and apply weights to each of them until they break. The mean breaking weight for the 45 cables is x=768.2 lb. The standard deviation of the breaking weight for the sample of cables is s = 15.1 lb.

In the example we concluded the following. We are 95% confident that the mean breaking weight for all cables of this type is between 763.7 lb and 772.7 lb.

In other words the 95% confidence interval is (763.7, 772.7).

1. Suppose the engineers want to make a 99% confidence interval. They plan to use the same sample of 45 cables. Use the applet to find the critical T-value they will use in the computation of the margin of error.

2. Construct the 99% confidence interval. Enter the lower bound of the interval (the smaller number). If necessary, round to two decimal places.

3. What is the upper bound of the 99% confidence interval? If necessary, round to two decimal places.