00:01
Hello, students.
00:02
So in this question, this is given that a british medical journal published the result of a study to compare the effectiveness of handwashing with soap and hand rubbing with alcohol.
00:12
So, the healthcare workers who used hand washing with soap, their main bacterial count is 121 and the standard division of disease 70, right? and the health workers who used hand rubbing with alcohol, their main bacterial count is 68 and the standard division of this, is 45.
00:32
Now we are given a random sample of 40 healthcare workers and this is said that mean bacterial count per hand is less than 49.
00:41
Okay.
00:42
Now we have to determine whether this sample of workers used hand rubbing with alcohol or hand washing with soap, right? so let's see how we can solve this.
00:52
So at first we will use the central limit theorem to determine the values.
00:57
Okay.
00:57
So i am writing down the central limit theorem.
01:00
So i can write.
01:01
By central by central limit theorem central limit theorem we can see that the x bar is approximately n of mu x bar right is equal to mu x this is central limit theorem and we can also write down the sigma x squared is equal to sigma x square is equal to sigma x square is equals to sigma x in a square multiplied by h x right so we will write down this is the central limit theorem basically we will down the values of each variable so this is x bar and this is approximately n of mu x bar and the value of mu x is given in this question and this is 121 and the sigma x bar square is equal to we can see that sigma x value of sigma x is already given and we can write down this as 70 and this is square.
02:10
So 70 squared divided by 40 is the value of sigma x bar square, right? so we will solve this gradually.
02:19
So this is already solved and mu x bar is already given and this is 121 and sigma x bar square is now 122 .5 after calculating.
02:32
Okay.
02:33
So this is given that this sample.
02:35
Of 40 health workers and this is said that the mean bacterial count per hand is less than 49.
02:42
So therefore the probability of x bar less than 49 will be as shown.
02:48
So, i mean probability of z less than.
02:53
So i'll out down a value so 49 and what is the value of mu x bar? this is 121 and what is the value of sigma x square? this is 122 .5.
03:04
So i will write down the value root over 122 .5, right? so this is is equals to probability of z less than if you calculate it carefully, it will become minus 6 .50.
03:19
Now if we use normal distribution values, the value of p will become as 3 .758.
03:28
So we can write down in the inside the bracket that we have used the normal distribution values.
03:35
Okay, so i am writing using normal distribution, using normal distribution values, right? so probability of hand washing with soap is already calculated.
03:56
Okay, now let's assume, now let's assume that the sample of 40 in question follows hand rubbing with alcohol, okay, so now assume that sample of 40, sample of 40 in question, sample of 14 in question follows hand rubbing, hand rubbing with alcohol, right? so let's assume the sample of 40 which is given in the question, the health workers use hand rubbing with alcohol, okay? so same, in the same way we have calculated the handwashing itself, we will also calculate the probability of hand rubbing with alcohol, okay...