SAT I scores around the nation tend to have a mean scale score around 500, a standard deviation of about 100 points, and are approximately normally distributed. What SAT I score within the population would have a percentile rank of approximately 16?
Im not sure how to do this...please help!!
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion (.16) and its Z score. (Remember that this Z score will be negative, because the percentile rank of 16 is below the mean.) Insert values into equation below.
Z = (score-mean)/SD
It doesn't show .16, it shows .15 as p-value of 0.4404 and z as 1.15....what do i do??
To find the SAT I score within the population that corresponds to a percentile rank of approximately 16, we can use the concept of z-scores. A z-score represents how many standard deviations a data point is away from the mean.
First, let's find the z-score corresponding to a percentile rank of 16. The percentile rank can be converted into a decimal, so 16% becomes 0.16. We can then use the z-score formula:
z = (x - μ) / σ
where:
- z is the z-score
- x is the SAT I score
- μ is the mean score (500 in this case)
- σ is the standard deviation (100 in this case)
Rearranging the formula, we can solve for x:
x = μ + (z * σ)
To find the z-score corresponding to a percentile rank of 16, we can use a standard normal distribution table or a calculator. In this case, the z-score corresponding to a percentile rank of 16 is approximately -0.994.
Now we can substitute the known values into the equation:
x = 500 + (-0.994 * 100)
x ≈ 400.6
Therefore, the SAT I score within the population that would have a percentile rank of approximately 16 is around 400.6.