Answer:
its 1/4 :)
Step-by-step explanation:
Answer: The correct mean is 161.
Step-by-step explanation: The question states that we have computed the mean of 40 observations and the mean is 160. This means the set of data altogether is 40 numbers. In order to arrive at the mean, we must have added all 40 observed data to get the summation of observed data and divided this by 40. In other words, we must have done something like,
Mean = {Summation} x/{x}
Where x = 40 and the mean computed is 160.
Therefore,
160 = {summation}x/40
By cross multiplication we now have
160 (40) = {summation} x
6400 = {summation}x.
However, we must not forget that one of the values in the observed data was wrongly copied as 125, (instead of 165). What this means is that the summation of all observed data is having a shortage of 40 (that is, 165 - 125). If we now insert the correct figure of 165 in place of the wrong one which is 125, our summation of observed data would now become 6440 (the shortage of 40 would have been added back to 6400).
What we now have is
Mean = {summation}x/x
Mean = 6440/40
Mean = 161
There are 
ways of building a subset of 
elements from 
, so the total number of subsets you can build is
Recalling the binomial theorem, the above sum is equal to
as required.
