Respuesta :
Answer:
A. 16th
Step-by-step explanation:
We have been given that on a normal distribution IQ test scores, with a mean of 100 and a standard deviation of 15 points. We are asked to find the percentile for a score of 85.
We will use z-score formula and normal distribution table to answer our given problem.
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
z = Z-score,
x = Sample score,
[tex]\mu[/tex] = Mean,
[tex]\sigma[/tex] = Standard deviation.
Upon substituting our given values in z-score formula, we will get:
[tex]z=\frac{85-100}{15}[/tex]
[tex]z=\frac{-15}{15}[/tex]
[tex]z=-1[/tex]
Now, we need to find area under a normal curve that corresponds to z-score of [tex]-1[/tex] that is [tex]P(z<-1)[/tex].
Using normal distribution table, we will get:
[tex]P(z<-1)=0.15866[/tex]
Let us convert 0.15866 into percentage as:
[tex]0.15866\times 100\%=15.866\%\approx 16\%[/tex]
Therefore, a score of 85 places you approximately in 16th percentile of the population.
