There are two major tests of readiness for college, the ACT and the SAT. ACT scores are reported on a scalefrom 1 to 36. The distribution of ACT scores for more than 1 million students in a recent high school graduatingclass was roughly Normal with mean ?? = 20.8 and standard deviation ?? = 4.8. SAT scores are reported on ascale from 400 to 1600. The SAT scores for 1.4 million students in the same graduating class were roughlyNormal with mean ?? = 1026 and standard deviation ?? = 209.Sonya scores 1310 on the SAT. Jerome scores 29 on the ACT. Assuming that both tests measure the same thing,who has the higher score? Report the z-score for both student and make sure to mark these on an appropriatenormal curve.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
There are two major tests of readiness for college, the ACT and the SAT. ACT scores are reported on a scale
from 1 to 36. The distribution of ACT scores for more than 1 million students in a recent high school graduating
class was roughly Normal with mean ?? = 20.8 and standard deviation ?? = 4.8. SAT scores are reported on a
scale from 400 to 1600. The SAT scores for 1.4 million students in the same graduating class were roughly
Normal with mean ?? = 1026 and standard deviation ?? = 209.
Sonya scores 1310 on the SAT. Jerome scores 29 on the ACT. Assuming that both tests measure the same thing,
who has the higher score? Report the z-score for both student and make sure to mark these on an appropriate
normal curve.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
