Question

data interpretation (ap psychology review unit 0 topic 3)

1. use the graph below to answer the following question on a set of test scores.

the mean of the class test scores is 100 and the standard deviation is 15.
what is the percentile rank for 130?

1. use the graph below to answer the following question.

the mean of the data set is 100 and the standard deviation is 15.
what is the percentile rank for 55?

graph: normal distribution with -4, -3, -2, -1, 0, +1, +2, +3, +4 on x - axis, percentages: 0.5% at -4, 2.0% at -3, 13.5% at -2, 34% at -1, 34% at +1, 13.5% at +2, 2.0% at +3, 0.5% at +4. text box: \if this is making sense take 5 seconds and try\ and \95%\ below

Explanation:

Sub - Question 1:

Step 1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 130$, $\mu=100$, and $\sigma = 15$.
$z=\frac{130 - 100}{15}=\frac{30}{15}=2$

Step 2: Determine the percentile rank using the normal distribution curve

Looking at the normal distribution curve, to the left of $z = 2$, we sum up the percentages: $0.5\%+2.0\% + 13.5\%+34\%+34\%+13.5\%=97.5\%$

Step 1: Calculate the z - score

Using the z - score formula $z=\frac{x-\mu}{\sigma}$, with $x = 55$, $\mu = 100$, and $\sigma=15$.
$z=\frac{55 - 100}{15}=\frac{- 45}{15}=-3$

Step 2: Determine the percentile rank using the normal distribution curve

To the left of $z=-3$, we sum up the percentages: $0.5\%$

Answer:

The percentile rank for 130 is $97.5\%$

Sub - Question 2: