00:01
This problem says the acme company manufactures widgets and the distribution of widget weights is bell -shaped and the widget weights have a mean of 41 ounces and a standard deviation of 6 ounces.
00:09
Use the standard deviation rule, also known as the empirical rule, to answer our three questions.
00:14
First, we're asked for what two weights that 99 .7 % of our widget weights would lie between.
00:20
This is one of the three values we get from the empirical rule, which tells us that within three standard deviations less to three standard deviations more than our mean, we hold 99 .7%.
00:31
So we have 99 .7 % here between the weight of 23 and the weight of 59.
00:38
For our next question, we want the percentage between 29 and 59, and we already saw that we have 59 as three standard deviations above.
00:45
And we also need to remember about our bell -shaped normal distribution that we have symmetry so we can find the percentage of half of our distances that are given from our empirical rule by taking that and dividing by two.
00:58
So that tells us that the percentage that falls within the mean and three standard deviations above would be half of 99 .7, which is 49 .85%.
01:08
And we want to combine that percentage with the percent that's between the mean and two standard deviations less, because that's where our 29 falls...