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 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.

Accepted Answer

(a) $137$; (b) $149.5$.

Median of normal distribution

Median of normal distribution