00:01
All right, this problem is going to involve the empirical rule, and it starts by saying that our data is normally distributed, so therefore we can draw that bell curve.
00:11
The mean is 25, with a standard deviation of 5.
00:16
So that means i'm going to add 5, and i'll get to 30.
00:20
I'll add 5 again, 35, and i'll add 5 again, and i'll get to 40.
00:25
I'll subtract 5, get to 20, subtract 5, 15, and subtract 5, 5 and i get 10.
00:32
Now what the empirical rule states is that within one standard deviation of the mean, so that means if i go one in each direction, it accounts for 68 % of the data.
00:47
So that means that going to the left and going to the right would be 0 .34 in each of those pieces.
00:58
The next thing that the empirical rule states is that if you go two in each direction, then it accounts for 95 % of the data.
01:11
So that means if i were to go to more out, this would be 0 .135, and this would be 0 .135.
01:24
And then the final part of the empirical rule says that if you go out 3 in each direction, it accounts for 99 .7 % of the data.
01:39
So that means if i go out one more in each direction, this little section here will be 0 .235, and right here would be 0 .235.
01:53
So let's answer the questions here.
01:55
So part a is asking you, what is the probability that the trip lasts more than 20 minutes.
02:09
So that means we are adding this section, this section, this section, this section, and this section.
02:19
Well, from here on up accounts for half, plus we have to add this little piece right here.
02:29
So therefore, the probability of the trip lasting more than 20 minutes is going to be 0 .84.
02:39
Let's do part b.
02:41
Part b is saying, what's the probability? that the trip lasts less than 15 minutes.
02:50
So that means we're talking about these two sections right here...