Question

Vending machines can be adjusted to reject coins above and below certain weights. The weights of legal U.S. quarters are normally distributed with a mean of 5.67 grams and a standard deviation of 0.0700 gram

The vending machine is adjusted to reject quarters that weigh more than 5.80 grams and less than 5.52 grams, what percentage of legal quarters will be accepted by the machine?

Answer 1

Let X be the weights of the quarters

X~ Normal ( 5.67, 0.07)

Percentage of legal quartes that will be accepted by the machine is= P( 5.52 < X < 5.8)

= P( < < )

= P( -2.14 < X < 1.86)

= P( z < 1.86) - P( z < -2.14)

= P(z < 1.86) - 1 + P(z < 2.14)

= 0.96856 - 1 +0.98382

= 0.95238

Thus 95.24% of the legal quarters will be accepted by the machine.