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2 Statistics

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Question 59

The amount of water W W\,W ml placed in a bottle is Normally distributed with mean 500 ml. It is known that P(W>504)=0.30P(W>504)=0.30P(W>504)=0.30.

a.

Find the standard deviation of WWW.

[2]
b.

Find k k\,k such that P(k<W<505)=0.45P(k<W<505)=0.45P(k<W<505)=0.45. The machine is adjusted and its population standard deviation becomes 6 ml. A manager believes that the population mean is now less than 500 ml. A random sample of 20 bottles has mean 498.1 ml.

[4]
c.

Test the manager's belief at the 5% significance level.

[7]
Markscheme

2 Statistics Questions

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

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