00:02
In this question, for part a, here we have what? here we have z is equals to x minus mu divided by sigma.
00:12
So, this value is equals to what? so, this value is equals to 58 minus 55 divided by sigma divided by 7.
00:21
So, this is equals to 3 divided by 7.
00:22
So, here the value is what? here the value is 0 .43.
00:28
Now, so we draw the graph for this.
00:32
So, here we have points 34, then 41, then 48, then we have 55, then we have 62, then 69, then 76, okay.
00:54
So, the graph will rise from here from 34 and it will rise at peak here over here, okay and it go up to 76.
01:03
So, we have shaded region between this, okay.
01:08
Within this part, we have the shaded region.
01:10
So, here t, that is probability for x is greater than 58.
01:18
This is equivalent to what? this is equivalent to or equal to we can say probability that is z is greater than what? z is greater than 0 .43.
01:31
So, here this value is equals to what? so, this value is equals to we have 0 .3341.
01:37
Now, we solve for the part b.
01:40
So, in part b here, what we have? we have z is equals to x minus mu divided by what? divided by sigma.
01:50
So, this value is equals to what? so, this value is equals to 43 minus 55 whole divided by what? whole divided by 7.
01:58
So, this value is equals to what? so, this value is equals to minus 12 divided by 7.
02:02
So, this is equals to what? so, this is equals to we have minus 1 .71.
02:09
Now, we draw the graph for this.
02:14
So, here the graph is like we have this similarly as a previous one, but the shaded region will change, okay.
02:21
So, here we have 34, then we have 41, then we have 48, then 55, okay, then we have here 62, then 69 and then 76, okay.
02:43
Similarly, in the previous one, it will be at peak at what? it will be at peak when it is it reached to 55.
02:50
So, it will move from here and peak at this point and it's go up to 76.
02:54
So, here we have a shaded region from this region to this region, because we have to find the what? we have to find the probability that is x is greater than 43.
03:07
So, this is equals to p for z is greater than what? z is greater than minus 1 .71.
03:13
So, this value is equals to we have 0 .9568...