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Problem 3. We destroy a number of concrete beams by applying a large tensile load. Each time, we write down the tensile strength of the beam from the test. We obtain the following data: 363 376 376 377 380 382 386 389 392 394 401 402 403 408 409 418 420 Assume that the tensile strength has a normal distribution, but we don't know the true mean or variance. Form a two-sided interval that you are 95% sure includes the population mean. Problem 4. Using the same data as in the previous problem, now assume that we're building a rather large bridge in an earthquakeprone region by using 50,000 of those beams. The bridge is designed with enough redundancy in the structure so that even if 10% of the beams fail in an earthquake, the bridge won't collapse. We want to nd a design tensile strength such that, with 95% condence, the bridge will remain standing after an earthquake. Form one of the intervals discussed in class to determine the design strength you should assume for this to be the case. Problem 5. Again using the same data, now imagine that we are building a rather small bridge using only one concrete beam, and we are curious about its strength. Obviously, we can't destroy it to nd out, because then we can't use it for the bridge. You want to identify a design strength you can assume with 95% condence. Form one of the intervals discussed in class to do this. Problem 6. Find a 95% condence interval for the true standard deviation of the strength of these beams. Problem 7. The previous four problems all relied on the assumption that the failure strength is normally distributed. What if this isn't true? Suggest a procedure we could follow to nd a 95% condence interval for the population mean strength in this case. (Imagine you do not have any time, budgetary, or other resource constraints.)