00:01
Hello student.
00:02
It is given that x follows normal distribution with mean mu is equal to 80 and variance is equal to 100.
00:10
Now here we have to find out the probability that x is greater than 60.
00:17
So here first we need to take a root of variance.
00:23
So here root of variance is equal to 10.
00:25
We have probability of x greater than 60 using empirical rule that is x minus mu.
00:31
60 minus 80 divided by 10.
00:34
Here 60 minus 80 divided by 10 is equal to 2.
00:38
Therefore probability of z greater than 2 is equal to 1 minus probability of z less than 2.
00:48
So using a table probability is equal to 0 .477.
00:56
Now subtracting it will gives the probability of z greater than 2 which is equal to 0 .5228.
01:04
Now here we have to find out the probability of x is less than 55.
01:11
Here probability of x less than 55 is equal to 55 minus 80 divided by 10.
01:21
Here 55 minus 80 divided by 10 is equal to minus 2 .5.
01:27
Therefore probability of z less than minus 2 .5...