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4 Unit A2 2: Applied Mathematics (A-level only)

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Question 93

A civil engineer tests the load-bearing capacity of a new alloy beam. The design specification requires a mean breaking load of 80.0 kN.

The engineer suspects that the mean breaking load has decreased, and tests a random sample of 50 beams. The breaking loads, in kN, are denoted by xxx, and

∑x=3992.5\sum x = 3992.5∑x=3992.5 and ∑x2=318810.5\sum x^{2} = 318810.5∑x2=318810.5

a.

Find the mean and the standard deviation of the breaking loads in the sample.

[3]
b.

Stating your hypotheses clearly, test at the 1% significance level whether there is evidence that the mean breaking load is less than 80.0 kN. You may assume that the breaking loads are Normally distributed with the standard deviation found in part (a).

[5]
Markscheme

4 Unit A2 2: Applied Mathematics (A-level only) Questions

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