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nbme23/Block 3/Question#37

A 48-year-old man is referred for evaluation of ...

108 to 118

+6  upvote downvote
submitted by sajaqua1(258),

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.

usmleuser007  How did you get the SD to be 1.5? +
usmleuser007  NVM Got it +

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

paulkarr  Glad I wasn't the only one to solve it this way...didn't even think to bother with the calculation. +

NVM got it.

Just FYI: 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

I tried to calculate it more precise, and messed up the answer...

Here is why:

• 99.7% CI = 3 SD
• However: 99.0% CI is actually 2.5 SD (or 2.57 if you want to be more precise)

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.