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2 Statistics

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Question 79

The volume V V\,V ml of juice in a carton is modelled by V∼N(505,3.782)V\sim N(505,3.78^2)V∼N(505,3.782).

a.

Find the expected number of cartons containing less than 500 ml in a batch of 1000. Give your answer to the nearest whole carton. The population standard deviation will remain 3.78 ml. A regulation requires no more than 1% of cartons to contain less than 500 ml.

[2]
b.

Find the minimum population mean that meets the regulation. Give your answer to 3 significant figures. The process mean is set to 509 ml. Later, a random sample of 100 cartons has mean volume 508.37 ml.

[3]
c.

Test at the 5% significance level whether there is evidence that the population mean has fallen below 509 ml.

[7]
Markscheme

2 Statistics Questions

  1. A Level
  2. /Maths
  3. /2 Statistics

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