Circular metal tokens are used to operate a washing machine in a Laundromat. The diameters of the to

Question

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. 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 two tokens out of $20$ will not operate the machine.

Accepted Answer

(a) $2.00, 0.0305$; (b) $0.736$.

Obtaining unknown mean and variance

Obtaining unknown mean and variance