00:02
For this question, there is a normal distribution here and the given mean value, which is denoted by mu, that is 12, and the standard deviation is 0 .6.
00:11
Let's say x is the random variable for this normal distribution, that is 12 and 0 .6.
00:17
Great.
00:17
So what we have to do, in part a, we have to find the x value is between x2 and x1, and it has the probable to 0 .95.
00:27
So we have to get the x2 and x1 values here.
00:30
Just remember the empirical rule.
00:33
So the empirical rule would be maybe more practical to find the answer here.
00:39
So for the empirical rule, let's say this is mu, and this is mu plus standard deviation, and mu plus two standard deviation, and this is mu minus one standard deviation, and mu minus two standard deviation.
00:52
So the area of this region, so the total area for this region, which is 95.
00:57
So that means x2 is equal to mu plus two standard deviation and x1 which is mu minus two standard deviation.
01:06
So the mu is given as 12 minus no plus two times 0 .6 which is equal to that is 13 .2 13 .2.
01:22
And for the x -1 value which should be this is 12 minus 2 times 0 .6 that should be 10 .8 so these are the two values that this random variable axis is between 13 .2 and 10 .8 that's it and what about for part b so for part b what we have to find we have to find for n is equal to 36 first of all, we need to just get the standard deviation for the sample space.
01:55
The formula for the standard division sample space, which is the standard deviation of the population, divided by the radical n, which is the number of terms in the sample.
02:07
So the standard deviation for the sample space, which is 0 .6, divided by radical 36, which is equal to 0 .1.
02:16
So let's say x is a random variable for this normal distribution.
02:21
So the mean value is the same with the population, that is 12, but standard division is 0 .1.
02:27
So we have to find the value for x is less than 11 .8...