Consider the following table, showing the official mean weight and estimated standard deviation for five U.S. coins. Suppose a vending machine is designed to reject all coins with weights more than 2 standard deviations above or below the mean. For each coin, find the range of weights that is acceptable to the vending machine. In each case, what percentage of legal coins is rejected by the machine? Assume the coin weights are normally distributed.

Transcribed Image Text:

Coin Penny Nickel Dime Quarter Half-dollar Mean weight (grams) 2.500 5.000 2.268 5.670 11.340 Estimated standard deviation (grams) 0.03 0.06 0.03 0.07 0.14