00:01
Hello students, it is given that 16 random independent normal variables are there.
00:10
The distribution of this 16 random variable normal variable have mean equal to 0 and variance equal to 1.
00:25
This 16 random variables follow normal distribution.
00:35
X bar is the average of these 16 random variables.
00:46
So x bar will follow normal distribution with mean same as the mean of the population which is 0 and standard deviation as sigma upon square root of n.
01:04
So it will have the distribution of x bar is normal with mean 0 and standard deviation will be sigma is 1 upon square root of 16 which is 4.
01:16
Now we have to find c such that probability of mod of x bar less than c is 0 .5.
01:26
It means probability of minus c less than x bar less than c.
01:35
Now let us try to show the given information on the normal curve.
01:44
So we have to find c such that probability between the minus c and plus c is 0 .5.
01:56
It means the probability left to the minus c and right to the plus c is 0 .5.
02:02
Now we know that the normal distribution is symmetric about the mean...