oscar recorded the amount of his monthly electric bill for the first 11 months of the year. an ordered list…
oscar recorded the amount of his monthly electric bill for the first 11 months of the year. an ordered list of the amount, in dollars, of his monthly bills is shown.\n79, 98, 99, 99, 102, 105, 119, 122, 124, 125, 127\noscar budgeted $110 per month for his electric bill.\nwhat would be the amount of his last monthly bill in order for the mean bill amount to be $110 for all 12 months?\na. $105\nb. $109\nc. $110\nd. $112\ne. $121
Answer
Explanation:
Step1: Calculate the total amount for 12 months
The formula for the mean (\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}). Given (n = 12) and (\bar{x}=110), then the total amount for 12 months is (\sum_{i=1}^{12}x_{i}=n\times\bar{x}). So, (\sum_{i = 1}^{12}x_{i}=12\times110 = 1320).
Step2: Calculate the sum of the first 11 - month bills
(79+98+99+99+102+105+119+122+124+125+127) (=(79 + 98)+(99+99)+(102 + 105)+(119+122)+(124+125)+127) (=177+198+207+241+249+127) (=(177+198)+(207+241)+(249+127)) (=375+448+376) (=375+(448+376)) (=375 + 824=1199).
Step3: Find the 12 - month bill amount
Let the 12 - month bill amount be (x). Then (x=\sum_{i = 1}^{12}x_{i}-\sum_{i = 1}^{11}x_{i}). Substitute (\sum_{i = 1}^{12}x_{i}=1320) and (\sum_{i = 1}^{11}x_{i}=1199) into the formula, we get (x=1320 - 1199=121).
Answer:
E. ($121)