calculations?

Question

two hosehols on the same street use the local utility company for energy needs . an investigator collects a years worth of monthly bills for the two hoseholds. for hosehold A, the average monthly is $150 with a standerd devation of $35. for hosehold B, the average bill is $200 with a standard devation of $25 . for wich household would it e easer to predict the bill from month to month ? please provide a detailed explanation .

Answer 1

The question says that the monthly bills are normally distributed as per the gaussian curve. So, 2 std dev would have 96% of all cases. i.e. ( + - 1 std dev on each side of the mean).

Now, coefficient of variation is defined as std dev / mean. This is the extent of variation in the data used to calculate the mean and std dev. Higher the CoV, more spread is the data. A smaller CoV means that the range of the data is smaller.

In this case, CoV is smaller for case B (25/200 = 0.125) than for case A (35/150 = 0.23)

So, it would be easier to predict the bill for house B.

Assumption: Strictly statisticaly speaking, this explanation assumes that the std dev and mean observed in the data for both household holds true (null hypothesis is accepted) for the "entire population" i.e. it can be used to predict values. If that is not the case, then this conclusion can not be made. It is possible that observed mean for Household A hold for the population while that for B does not.

Answer 2

In abt 96% of the cases the bill will be 2 times the standard deviation from the average (more or less). This would mean that in case of household A the difference can be 70/150=46,66% more or less. In case B it is 50/200=25% more or less. As the percentage of B is lower than A, it is easier to predict the bill for household B from month to month

Answer 3

Easier for household B. It has an average of 200, and 67 percent of all monthly bills fall between 175 and 225, while 96 percent fall between 150 and 250.

Household A has a lower bill, but the range is bigger, with 96 of bills falling between 80 and 220.

Answer 4

The smaller the standard deviation the easier it is predict the result. With no standard deviation you know the bill will be $200, but it's give or take $25.

Answer 5

household B. because u can multiply in your head much more easily with 200. it's just like counting in 2's except 2 extra 00s.and $25 is also easier 2 count than $35 multiplied. do u get it? :)

Answer 6

The smaller the standard deviation, the closer it's likely to be to the average price. House B has a smaller deviation, so it's house B.