We destroy a number of concrete beams by applying a large tensile load. Each tim

Question

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. We are curious about the average strength of the beams, and want to find a two-sided interval that we are 95% sure includes the true average. A)What is the interval? now assume that we're building a rather large bridge in an earthquake-prone region by using 500 of those beams. we add enough redundancy to the structure so that even if 10% of the beams fail in an earthquake, the bridge won't collapse. We want to find a design tensile strength such that, with 95% confidence, the bridge will remain standing after an earthquake. B) Use what you have learned about intervals to identify a design strength can we use, such that only 10% of the beams would be weaker than the chosen design strength. 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 find out, because then we can't use it for the bridge. C) What is the maximum tensile load we can apply to the beam if we want to be 99% confident that it will not fail?

Explanation / Answer

From the given data we have

a)

b)

z-value = 1.28

xbar = mean - z*sigma/sqrt(n)
xbar = 392.7059 - 1.28 * 15.661/sqrt(500)
xbar = 391.8094

C)
z-value = 2.33

xbar = mean + z*sigma/sqrt(n)
xbar = 392.7059 + 2.33 * 15.661/sqrt(500)
xbar = 394.3378

xbar 392.7059 std.dev. 15.66098

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