Question 1206898
the 68-95-99.7 rule states that:


68% of the z-scores are within 1 standard deviation from the mean.
95% of the z-=scores are within 2 standard deviations from the mean.
99.7% of the z-scores are within 3 standard deviations from the mean.


the empirical rule chart is broken down as shown below.


<img src = "http://theo.x10hosting.com/2024/041203.jpg">


within 1 standard deviation from the mean is 2 * 34 = 68%.


within 2 standard deviations from the mean is 2 * (34 + 13.5) = 95%.


within 3 standard deviations from the mean is 2 * (34 + 13.5 + 2.35) = 99.7%.


the raw score is 43 and the mean is 52 and the standard deviation is 9.


z-score formula is:


z = (x - m) / s


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


your z-score is (43 - 52) / 9 = -9/9 = -1.


the area to the left of that z-score is .15% + 2.35% + 13.5% = 16%.


that's a ratio of .16.


if you use a z-score calculator, you would get what is shown below.


<img src = "http://theo.x10hosting.com/2024/041204.jpg">


that rounds to .1587 which is pretty close to .16.


that's less than 1% off of the actual.