00:01
After 1964 quarters were manufactured so that their weights have a mean of 5 .76, excuse me, 5 .67, i inverted those 5 .67 grams, and a standard deviation of 0 .006 grams.
00:17
Some vending machines are designed so that you could adjust the weights of quarters that are accepted to keep people from using any round objects of the right size.
00:24
If the machine is accepting a lot of counterfeit coins, it can be adjusted to accept a smaller range of acceptable weights.
00:31
This should reduce the number of counterfeit coins accepted, but it also increases the legal coins that are rejected.
00:37
What interval of weights will only reject the lowest 1 % and the highest 1 % of legal coins? so the lowest 1 % we're going to look in our standard normal table, and we're going to find a z score of negative 0 .233.
00:58
And the 99th percentile, or 0 .99, would be the highest 1%, so that's positive 2 .33.
01:07
And we're going to calculate these values by taking our mu of 5 .67 plus our sigma of 0 .006 times the z score that we just found.
01:22
So for the 99th percentile, it'll be 5 .67 plus 0 .006 times positive 2 .33.
01:28
And that gives us 5 .656 and 5 .684.
01:38
And that would be our interval, 5 .656 to 5 .684.
01:46
Next, we are going to talk about if we set the weights, the weight restrictions to 5 .665 and 5 .695, what percentage of quarters will be rejected? so really we're asking for, we're asking for the percentage, that would be outside of.
02:08
So things that would be smaller than 5 .665 or larger than 5 .695.
02:21
So in this case, we're going to take the probability that z is less than 5 .665 minus 5 .67 divided by 0 .006...