For this question, they want you to know the percentages of values that fall within 1, 2, and 3 standard deviations from the mean in a normally distributed set of values. In general, 68% of values fall within 1 standard deviation of the mean, 95% fall within 2 standard deviations, and 99.7% fall within 3 standard deviations.
Knowing this, we look at the bounds that the vending machine will accept. They are 0.11g above and 0.11g below the mean. The standard deviation of the distribution is 0.062. If we double the standard deviation, we get 0.124 (which is very close to 0.11). Thus, we can see that the vending machine accepts coins just about two standard deviations from the mean. Since we know that 95% of data points in a normal distribution fall within 2 standard deviations, we can say that about 95% of coins should be accepted theoretically.
95% of 300 coins is 285, so we expect 15 coins to be rejected.
