Could you please solve these problems? Please help me by answering and showing explanations.

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