Question 1104234
mean = 1200
standard deviation = 300
sample size = 12


standard error = standard deviation of population / square root of sample size = 300 / sqrt(12) = 86.60254038.


z-score = (x-m)/s


x is the raw score
m is the raw mean
s is the standard error.


z = (1100 - 1200) / (300/sqrt(12)) = -1.154700538


using a z-score calculator, the probability of getting less than a z-score of -1.154700538 is equal to .1241065934.


the probability of getting more than a z-score of -1.154700538 is equal to 1 - .124065934 = .8758934066.


the closest selection is .8749.


your problem more then likely used rounded numbers so i would guess that selection 4 is correct.


if i rounded the z-score to -1.15, i would get .8749280114 which equals .8749 rounded to 4 decimal places.


confirmation that this is correct can be made through this online calculator at <a href = "http://davidmlane.com/hyperstat/z_table.html" target = "_blank">http://davidmlane.com/hyperstat/z_table.html</a>


first  picture is the raw score results.
second picture is the not rounded z-score results.
third picture is the rounded z-score results.


<img src = "http://theo.x10hosting.com/2017/121001.jpg" alt="$$$">


<img src = "http://theo.x10hosting.com/2017/121002.jpg" alt="$$$">


<img src = "http://theo.x10hosting.com/2017/121003.jpg" alt="$$$">


as you can see, raw results and no rounding of the z-score results in .8759, while rounding the z-score results in .8749.


if you solve the problem and you're close to one of the results, but not right on, consider the difference may possibly be due to rounding.