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Median of normal distribution

Median of normal distribution

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 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 \(2\) tokens out of \(20\) will not operate the machine.

Solution:

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Answer:(a) \(\mu\approx2.00\text{ cm}\), \(\sigma\approx0.0305\text{ cm}\) (3 s.f.; unrounded \(\mu=2.002637490\ldots\)). (b) \(0.736\) (3 s.f.), under the independent-token model.

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