A standard deviation is a measure of probability in resembling the average. One standard deviation on a bell curve distribution creates a 67% chance that the answer will lie in there. Two standard deviations will create a 95% chance. Three standard deviations creates a 99.7% chance.
This patient has an average of 113, and a 95% confidence at 110-116 means that the SD is 1.5 . So one additional SD would give us a range of 108.5-117.5, rounded to 108-118.
NVM got it.
the CI was stated to be from 110-116 with 95% and mean of 113.
So, on either there are two SD on either sides of 113 (the mean) that give the 95%.
116-113= 3 within 2SD above the mean
113-110= 3 within 2SD below the mean
3 divided by the 2 SD = 1.5 per SD.
to get from 95% to 99% you have to incorporate one more SD (3 SD) on either sides of the mean (113)
Therefore; at 99% CI 110-1.5= 108.5
CI 116+1.5= 117.5
Round these up and you get 108-118
So a simpler way than all the math being done is understanding what CI means.
CI - range of values w/in which the true mean of the population is expected fall
So a CI of 95% will be more precise and have a narrow range compared to a CI of 99% will be less precise because its including more values in and result in a wider range.
So if CI of 95% is 110 to 116 then a CI of 99% has to be a range that is wider... 108 to 118
I tried to calculate it more precise, and messed up the answer...
Here is why:
1 SD = 1.5 mmHg → 2.5 SD = 3.75 mmHG
This results in a 99% CI of 109.25 (113-3.75) to 116.75 (113+3.75)
Closer to answer C than B.