Question 1085500
the mean is 7 and the standard deviation is 5.


if you want a probability of 34% to be between certain limits of the normal distribution curve, then you will have 100% - 34% = 66% outside of these limits.


cut that in half and you will have 33% outside the left limit and 33% outside the right limit


33% outside the right limit is to the right of that limit.


this means that 67% is to the left of that limit.


you want to find the z-score for that right limit.


look in the z-score table for a percentage of 67% to the left of the z-score.


that would be a ratio of .67 that you're looking for.


you can also use a calculator, which is a lot easier.


we'll use the table for now to see what we get.


the table shows a ratio of .67 is associated with a z-score of .44


.44 has 33% of the area under the distribution curve to the right of it.


since the distribution table is symmetric, then -.44 has 33% of the area under the distribution curve to the left of it.


so limits are a z-score of -.44 to .44


your mean is 7 and your standard deviation is 5


you want to relate your z-score to your raw score.


the formula to use is z = (x-m) / s


z is the z-score
x is the raw score
m is the raw score mean
s is the standard deviation.


in your problem, the formula becomes


-.44 = (x-7) / 5 and .44 = (x-7) / 5


solve for x in each of these and you will get:


x = 5 * -.44 + 7 and x = 5 * .44 + 7


your raw score limits will be between 4.8 and 9.2


with these limits, 34% of the area under the normal distribution curve will be between them.


visually, this looks like this:


<img src = "http://theo.x10hosting.com/2017/062001.jpg" alt="$$$" </>


it looks like it's a little off because the area shows as .3401.


that's due to rounding.


i used a calculator and got the following limits.


4.800434151 to 9.199565849


visually that looks like this:


<img src = "http://theo.x10hosting.com/2017/062002.jpg" alt="$$$" </>


you can see that the area between shows as .34 which is a lot closer.