Finding data given sample mean and variance

#1
Hello,

I have a problem, I am given the sample size, mean, variance, and I know it is normally distributed.
The question states that 160 individual's BMI were measured. The sample mean was 27.9 and the variance is 26.01 and it is normally distributed.

1. I am trying to find the standard deviation-- is the variance just the square root of the SD??

2. And then the percentage of individuals that fall between 22.8 and 33.

3. How many SD above the mean is 30?

4. what is the upper and lower bounds given a 95% CI?

Thank you, I feel like there is a simple way to calculate but for some reason I have been struggling. Any help would be so appreciated.
 

hlsmith

Omega Contributor
#2
Yes, you can answer all of these questions given those parameters, and yes the SD is just the square root of the variance.
 
#3
The most helpful thing you can do is draw a picture of the normal curve with two horizontal scales - an x scale with real life numbers and a z scale with normal table numbers. Put in what you know. Shade in any area you are interested in.
Convert from one scale to another using either z = (x-m)/s or x = m+zs
Convert from an area to a z number and back using the normal table.