00:01
Hello students, we are asked in the question, what is the z score that is for the value that is two standard deviation away from the mean right? so let's start with our answer.
00:11
What we need to write is here normal distribution is there.
00:15
So in normal distribution what happens is how can we say this is normal distribution because here z score is given so this is the identification of normal distribution in normal distribution what happens is all the random variables are are distributed amongst bell shaped curve.
00:35
So basically this is plus z, this is minus z, this is b z.
00:39
Sum of all probabilities under normal distribution is one.
00:42
It means total area is equivalent to probability, which is also equals to one right and side area is point five, left -hand side area is point five.
00:50
It means area symmetric about y -axis.
00:52
So if i write here for this, here z score attribute is x minus mu divided by sigma, it means x is equal to x is equal to mu plus minus z sigma right this is j and this is sigma and let's say if it is negative then we can easily say that x must be if j is negative then x must be mu plus minus z sigma right now let us come to our empirical rule empirical rule says that probability of z value sorry x value is between mu minus sigma and mu plus sigma right and one sigma is equivalent to 60 % of the distribution 68 % of the distribution which is 60 .68 so let's say this is x is equal to mu where z is equal to zero this is x minus mu sorry x is equal to mu minus sigma it is mu plus sigma it is mu plus two sigma it is mu minus two sigma it is mu minus three sigma it is mu plus three sigma here it represent jad values so this is basically z values as we have already told this is z value so what does it mean according to empirical rule this is the first case in the second case probability if x is between mu two sigma so basically z value for this here and mu plus two sigma this value this value will falls under 95 % of the distribution.
02:31
It means 0 .5.
02:33
If i denote this, we can understand this by exploring something like this.
02:38
So let's say this is and this.
02:40
So basically 68 % of values lies under this and 95 % of the values lies under this...