stat theory says approximately 68% of measurements lie between +- one standard deviation. assume we have 100 students in our class. if in midterm 1 the mean score is 80 and standard deviation is 6, and you scored 86. approximately how many students scored below you?

since 86 is 1 std above the mean, that means that 34% are within 1 std above and below. That leaves 16% more than 1 std above or below the mean.

So, starting all the way out to the left, we have

16% more than 1 std below 80
68% within 1 std of 80
So, 84% scored below 86, or 84 students

How did you get 34% and 16%? Thanks

come on, man!

34% is 1/2 of 68%
34% above the mean, 34% below the mean.

Subtract the 68% from 100% leaves 32% outside 1 std.

16% way below the mean, 16% way above the mean.

To find out approximately how many students scored below you, we can use the properties of a normal distribution.

1. First, let's compute the z-score for your score of 86. The z-score indicates how many standard deviations your score is from the mean. It can be calculated using the formula: z = (x - μ) / σ, where x is your score, μ is the mean, and σ is the standard deviation.
z = (86 - 80) / 6
z = 1

2. The z-score tells us that your score is one standard deviation above the mean, which means approximately 84% of the students scored below 86 (according to the empirical rule of 68% + 16% + 2.5%).

3. Since we have 100 students in total, approximately 84% of them scored below you.
Number of students scoring below you = 100 * 0.84
Number of students scoring below you ≈ 84

Therefore, approximately 84 students scored below you.