00:01
Okay, in this question, we're given the following information, a mean of 100, a standard deviation of 10, and we're told we're dealing with a normal distribution.
00:11
Okay, looking at part a, we were trying to figure out what is the probability that x is greater than 70? okay, so what you would want to do here is calculate a z score first, and i have the z score formula listed here, so we would be doing 70 minus 100.
00:36
Divided by 10.
00:40
So that's negative 30 divided by 10 or negative 3.
00:45
And we want the probability that we're greater than 70.
00:48
So here is 70.
00:52
And what we just found is that that's a negative 3z score.
00:56
Now i see you have the opportunity in this question to use tables.
01:00
I'm going to show you how to do that with the table here.
01:03
So let's take a look.
01:05
I'm looking for a z score.
01:08
Let me back up one second.
01:09
What we will see in a z table is when i look up a negative three, it's going to give me the area here.
01:18
But we want to be the other side of it because we're supposed to be greater than 70.
01:22
We would want the area in this region.
01:26
So we're going to have to take what we're given from the z table and subtract it from one.
01:33
That's the basically the percentage we're getting as a decimal from the z table.
01:39
We will subtract it from 100 % or 1 when we get there.
01:43
Okay.
01:45
So let me jump over to my z table looking for a negative 3.
01:55
Okay.
01:57
This table has the positive values.
02:00
Now i'm looking for the table that has the negative values.
02:03
Now i want a negative 3.
02:05
And it's exactly negative three.
02:08
So i see it right here.
02:13
That is our area.
02:14
Okay? so i found that as a negative three, and i wanted the, this tells you what's in the hundreds place.
02:22
That's negative 3 .0, according to that, which is exactly what we wanted.
02:28
Okay, so i'm going to take that number, 0 .0013, back to the other screen.
02:38
So negative, i'm sorry, 0 .0 .0.
02:43
013, and that represents this area to the left of negative 3, but we want greater than that.
02:50
So our final answer should be 1 minus that, 1 minus 0 .003, which works out to 0 .997.
03:10
Okay, so that's part a.
03:14
Part b, we want to be less than 95%.
03:19
Less than 95%.
03:20
So let me fix the drawing i have up here.
03:31
And we would expect 95 to be very close to 100.
03:35
And this time we do want the area left of it.
03:39
We want over here less.
03:42
Okay, so moving on to that, i need to first calculate a z score.
03:47
That would be 95 minus 100 divided by 10.
03:52
That is negative 5 over 10, or negative 0 .5.
04:00
And when we go to the z table this time, because the z table is set up to give us the areas to the left of the z score, we won't have to subtract this one from one.
04:10
Okay, going to check the table now.
04:13
I'm looking for the negative 0 .5, which is right here, and we want to stay in the first column because we don't want a thousandth value.
04:24
So this one looks like 0 .3 .3.
04:27
0 .3085.
04:30
0 .3085.
04:40
Okay, so now in part c, we get a little tricky.
04:43
Let me fix the drawing up here.
04:58
Okay, so this time we want the probability of being less than 85, so here's 85, or greater than 125.
05:10
125 would be up around in this area.
05:16
Now, there's a couple approaches we could do here, but we want this area, and we want to this area.
05:26
So my plan would be to first find the z scores for both of them.
05:32
So let's go ahead and do that.
05:35
For the 85, it would be 85 minus 100 divided by 10.
05:43
That's going to be negative 15 divided by 10 or negative 1 .5.
05:49
I'm going to write that up here as negative 1 .5.
05:54
Now let's do the 125.
05:59
It by 10, 25 over 10, or 2 .5.
06:06
And that would be here.
06:09
All right, so my plan is to go to the z table, and i can easily find, i can easily find this value...