00:01
Hello, welcome to this lesson.
00:02
In this lesson, we have a mean of population.
00:10
We have a sample that is drawn for a population with a mean of 112.
00:17
The standard elevation of 40, the sample size that is 50.
00:23
So the first thing that we are looking for is the standard error.
00:30
Right so the standard arrow standard arrow is equal to the standard deviation all over the square root of the sample size so here we have 40 all over the square root of 50 here 40 divided by a square root of 50 to 2 the small places we have 5 we have 5 .66 all right the next thing that we are looking for is finding a probability that a sample mean is between 110 and 114 right so here we have z i that is equal to x minus the mean all about a standard deviation so after getting the z score you will look at it from the table the z table so here we have z that is equals to that is between 110 and 14 so you look at 110 minus the mean which is 112 all over the standard deviation which is 40 so here we have 110 minus 112 divided by 40 which is negative 0 .0 4 then we have z two which is the next z that we are looking for is 114 the next x is 114 minus 1 1 2 or 40 essentially we are looking at those 114 114 110 okay the probability that we have the mean between this okay so with this one we have one we have one 1 4 minus 112 and that is 2 on 40 so this is 0 .05 all right so you're finding the probability that z z is between negative 0 .05 and 0 .0 so this is equal to p z is less than 0 .05 minus the probability that we bring it so z is less than 0 .05 minus the probability that z is less than negative 0 .05 so let's check that from the table looking at negative 0 .05 to the 0 this is 0 negative 0 .05 here that would be 0 .4806 okay 0 .4806.
05:31
Okay, 0 .4806.
05:34
Absolutely for the positive one.
05:39
Alright.
05:46
Okay, so for the positive one, we have here 0 .005 and that is 0 .5 so 0 .5199, right? so 0 .5199 minus 0 .4806.
06:24
To two the small places, we have 0 .04...