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5 marksSampling Distribution and Estimation

CAPE Applied Mathematics Unit 1 · 2013 · Paper 2 · Question 5(a)(ii)

Random variable X is normally distributed with mean 35 and standard deviation 10. A sample of 8 observations is taken.

Calculate P(X̄ ≥ 38.7).

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  1. 5(a)(i)State the distribution of the sample mean, X̄, giving the value of its parameters.[3 marks]
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  4. 5(c)(i)State TWO conditions why a t-test will be appropriate to test the hypothesis that the machine is not dispensing on average 10 ounces of coffee.[2 marks]
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  6. 5(c)(iii)Test at the 5% level of significance whether the machine is dispensing on average 10 ounces of coffee.[7 marks]

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