Nina and Amy began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Nina took a test in English and earned a 71.8, and Amy took a test in Social Studies and earned a 60.7. Use the fact that all the students' test grades in the English class had a mean of 71.7 and a standard deviation of 11.7, and all the students' test grades in Social Studies had a mean of 60.6 and a standard deviation of 10.5 to answer the following questions. a) Calculate the z-score for Nina's test grade. z = z= b) Calculate the z-score for Amy's test grade. z = z= c) Which person did relatively better? Nina Amy They did equally well.
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.
Nina and Amy began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Nina took a test in English and earned a 71.8, and Amy took a test in Social Studies and earned a 60.7. Use the fact that all the students' test grades in the English class had a mean of 71.7 and a standard deviation of 11.7, and all the students' test grades in Social Studies had a mean of 60.6 and a standard deviation of 10.5 to answer the following questions.
a) Calculate the z-score for Nina's test grade.
z
=
z=
b) Calculate the z-score for Amy's test grade.
z
=
z=
c) Which person did relatively better?
Nina
Amy
They did equally well.
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 6 images
