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 operate the machine.
- Find the mean and the standard deviation of the distribution given that \(2\%\) of the tokens are too small and \(3\%\) are too large.
- Find the probability that less than \(2\) tokens out of \(20\) will not operate the machine.
Solution:
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Answer:(a) Mean \(2.00\text{ cm}\), standard deviation \(0.0305\text{ cm}\) (3 s.f.; unrounded mean \(2.002637490\ldots\text{ cm}\)). (b) \(0.736\), assuming independent sampling from the stated distribution.
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