00:01
There is given a normal distribution.
00:02
The main value was given here, which is denoted by mu, that is 68.
00:07
And the standard deviation, denoted by sigma here, which is equal to 17.
00:12
So this is an approximately normal here.
00:15
So we have to just make some approximation for the values, which is normally distributed, 16 and 17.
00:21
So in the first part of the question, we need to find the random variable x, which is at most 68, which means this is less than ever equal to 68.
00:29
If we just do for some approximation here, we're going to add 0 .5.
00:34
So i have to find which is less than 68 .5.
00:38
To get this probability, i'm going to use the normal cdf function.
00:42
So there is no lower boundary put negative 1a99.
00:45
The upper boundary is 68 .5.
00:47
So the mean is 68 and the standard division, which is 17.
00:51
Let me get the answer.
00:52
Press second variance and the second option, normal cdf, negative 1, second 899.
00:57
So the upper boundary is 68 .5 and the mean is 68 and the standard division which is 17.
01:05
So the answer would be 0 .51 and 17.
01:10
And what about for second i? so in this case, the speed is less than 68.
01:17
So less than 68 means the axis is not included 68, which is less than 68.
01:23
If i do the approximation, i'm going to just subtract 0 .5 value here, which would be axis less than 67 .5.
01:31
Again, i'm going to use the normal cdf here.
01:36
So the lower boundary, the upper boundary, and the mean, and the standard division.
01:43
Let me get the answer.
01:45
So i'm going to take the same value with the previous one.
01:48
I'm going to just change the upper boundary, which is 67 .5.
01:53
So the answer would be 0 .48 and 80, which is 3.
01:59
And what about for the 3? so for third eye, the answer here, for this part, we have to find the random variable x, which is between 85 and 34.
02:14
Again, if i do the approximation here, i have to take the lower boundary as 34 .5, less than x, less than.
02:22
This is 84 .5.
02:25
Again, i'm going to use the normal cdf.
02:28
So the lower boundary, the upper boundary, and the mean value.
02:33
68 and the standard division 17.
02:37
Let me get the answer press second variance.
02:41
Normal cdf lower boundary 34 .5 upper boundary 84 .5.
02:46
The mean is 68 and the standard division 17.
02:49
So the answer would be which is 0 .80 and 97.
02:54
This is the answer we have.
02:56
And what about for the fourth part here? so in this case we have to find the axis greater than 119.
03:04
If i do the upper here, which would be x is greater than 119 .5...