 Hello and welcome to the session. In this session, we are going to discuss the following question and the question says that the mean wage of 100 workers in a factory running two shifts of 70 and 30 workers is $40. The mean wage of 70 workers in the modeling shift is $38. Find the mean wage of 30 workers working in the evening shift. We know that when two sets of scores have been combined into a single distribution, then the mean of the combined distributions is the weighted mean of the means of the components. Therefore, mean of the combined distributions x bar is given by n1 x1 bar plus n2 x2 bar whole divided by n1 plus n2, where x bar is the mean of the combined distributions x1 bar and x2 bar are the means of the component distribution n1 n2 is the total frequency of the component distribution. With this key idea, we shall proceed with the solution. Now, the mean wage of 100 workers in a factory is given as $40. The workers work in two shifts such that 70 workers work in the morning shift and 30 workers work in the evening shift. Also, the mean wage of 70 workers is given as $38. We need to find the mean wage of 30 workers working in the evening shift. Let x bar, x1 bar and x2 bar denote the mean wage of 170 and 30 workers respectively. Then, the mean wage of 100 workers that is x bar is given as $40, the mean wage of 70 workers that is x1 bar is given as $38 and we need to find the mean wage of 30 workers also let n1 and n2 denote the number of workers working in the morning evening shifts respectively. Then, n1 is equal to 70 and n2 is equal to 30. Now we shall find combined mean of the wages of the workers using the key idea which states that when two sets of schools have been combined into a single distribution then the mean of the combined distributions is the weighted mean of the means of the components that is mean of the combined distribution denoted by x bar is equal to n1 x1 bar plus n2 x2 bar whole upon n1 plus n2 where x1 bar and x2 bar are the means of the component distribution and n1 plus n2 is the total frequency of the component distribution. Therefore, combined mean of the wages of the workers is given by x bar is equal to n1 x1 bar plus n2 x2 bar whole upon n1 plus n2 which is equal to x bar is 40 is equal to n1 x1 bar that is 70 into 38 plus n2 x2 bar that is 30 into x2 bar whole upon n1 plus n2 that is 70 plus 30 or we can write 40 is equal to 2660 plus 30 x2 bar whole upon 100 which can be written as 4000 is equal to 2660 plus 30 x2 bar which can be written as 4000 minus 2660 is equal to 30 x2 bar on solving further we get the value of x2 bar is equal to 1340 by 30 which is further equal to 44.66 or we can say the value of x2 bar is approximately equal to 44.7 Therefore, the mean weight of 30 workers in the evening shift is 44.7 dollars which is the required answer. This completes our session hope you enjoyed this session.