The most common intelligence quotient (IQ) scale is normally distributed with mean 100 and standard deviation 15. What score would put a child 3 standard deviations above the mean
Please see my answer below.
To find the score that is 3 standard deviations above the mean, we need to calculate the z-score first. The z-score measures how many standard deviations a value is away from the mean.
The formula to calculate the z-score is:
z = (x - μ) / σ
Where:
x is the score you want to find,
μ (mu) is the mean,
σ (sigma) is the standard deviation.
In this case, the mean (μ) is 100, the standard deviation (σ) is 15, and we want to find the score that is 3 standard deviations above the mean.
Plugging these values into the formula, we get:
z = (x - 100) / 15
We know that we want to find the score 3 standard deviations above the mean, so we set the z-score equal to 3:
3 = (x - 100) / 15
Now, we can solve for x:
3 * 15 = x - 100
45 = x - 100
x = 45 + 100
x = 145
Therefore, a score of 145 would put a child 3 standard deviations above the mean on this IQ scale.