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Obtaining unknown mean and variance

Obtaining unknown mean and variance

IB Year 6 | Grade 12

Circular metal tokens are used to operate a washing machine in a Laundromat. The diameters of the tokens are known to be normally distributed. Only tokens with diameters between \(1.94\) and \(2.06\) cm and operate the machine.

  1. Find the mean and the standard deviation of the distribution given that \(2\%\) of the tokens are too small and \(3\%\) are too large.
  2. Find the probability that less than two tokens out of \(20\) will not operate the machine.

Solution:

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Answer:(a) Mean \(2.00\ \mathrm{cm}\), standard deviation \(0.0305\ \mathrm{cm}\) (3 s.f.). (b) \(0.736\), assuming independent tokens with the same diameter distribution.

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