00:04
Okay, we're going to start with these experimental rocket burn times.
00:09
We're given a mean of 4 .76 seconds, so deviation of 0 .04 seconds.
00:15
And they told us it was a normal distribution.
00:17
So because they say it's a normal distribution, we can treat the random variable just like a random normal distribution.
00:27
So for this one, it says less than 4 .66 seconds.
00:32
So this is our normal distribution.
00:34
Remember, this is the mean, 4 .76.
00:37
And 4 .66, i don't know, is over here somewhere.
00:43
And then we are looking for this area here that's less than it.
00:52
Three easy steps for solving normal distribution.
00:55
First, find the z score.
00:58
Z score is the data point minus the mean over the standard deviation.
01:03
So we're going to take this data point that we're interested in.
01:06
4 .66 minus the mean.
01:12
Over standard deviation.
01:15
And this is going to equal our z score.
01:21
So our z is equal to negative 2 .5.
01:34
Okay? so that was step one.
01:36
Find the z score.
01:37
Use this formula, plug it in, find the z score.
01:40
And now from here we're going to go to the table.
01:43
So there's a z table here.
01:46
It has the normal, or the z scores on the outside.
01:49
And probabilities on the inside.
01:54
And notice up here it says that the z score, the probability, the numbers for the probability is everything less than the z value.
02:03
Okay? and our z score was negative 2 .5.
02:07
So we're going to look down this column for negative 2 .5.
02:11
And since the 100th place would be a 0, from the table we get 0 .0062.
02:25
So the probability of the rocket burn time being less than 4 .66 seconds is 0 .0062.
02:37
Just a little more than half a percent.
02:42
Okay.
02:44
So then for b, we're going to go about the same process.
02:49
But this time, our numbers are a bit different here.
02:52
So our means still in the middle, 4 .76.
02:56
But now we have 4 .8.
02:59
Let's just erase the mean sorry 4 .8 and we want this area everything that's greater than that perfect and so we're going to do the same thing now we didn't have to subtract in this first one we are going to have to subtract in this one i want you to think about why as i go on so z is equal to the data point minus the mean over the standard deviation.
03:48
And this time we get a z score of one.
03:52
That's a terrible one.
03:56
1 .00.
03:59
Okay? so we have our z score, and now we go to the table.
04:08
We're going to go to the table here.
04:11
Z score.
04:12
1 .0.
04:13
So i'm looking on the outside.
04:15
1 .00.
04:20
0 .8413.
04:28
Now, as you look at this, you should be like, this data, this blue space doesn't look like 84 % of the data.
04:39
This is where we need to subtract.
04:41
Remember i said that this is less than, not greater than.
04:45
It only does left tail.
04:47
It does not do the right tail.
04:49
So if we want to do the right tail, we have to subtract.
04:54
We're going to take 100 % of the data.
04:56
Data and subtract the less than part to give us the greater than part.
05:07
So we end up with about 16%.
05:14
So this area here is about 16%.
05:22
All right.
05:23
And then the last one for this problem, 4 .7 and 4 .82.
05:29
So we're doing between 4 .7, 4 .82.
05:43
Okay.
05:44
So we want to to find the area in between these.
05:48
We're not going to treat this any differently than the ones we've already done.
05:54
Okay? so we're going to start by finding the z scores for each of these...