Emily and Hillary began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Emily took a test in Math and earned a 71.2, and Hillary took a test in Art History and earned a 69.7. Use the fact that all the students' test grades in the Math class had a mean of 74.3 and a standard deviation of 9.3, and all the students' test grades in Art History had a mean of 66 and a standard deviation of 7.9 to answer the following questions. a) Calculate the z-score for Emily's test grade. 2 = [Round your answer to two decimal places.] b) Calculate the z-score for Hillary's test grade. 2 = [Round your answer to two decimal places.] c) Which person did relatively better? O Emily Hillary 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.
![Emily and Hillary began arguing about who did better on their tests, but they couldn't decide who did
better given that they took different tests. Emily took a test in Math and earned a 71.2, and Hillary took a
test in Art History and earned a 69.7. Use the fact that all the students' test grades in the Math class had a
mean of 74.3 and a standard deviation of 9.3, and all the students' test grades in Art History had a mean of
66 and a standard deviation of 7.9 to answer the following questions.
a) Calculate the z-score for Emily's test grade.
[Round your answer to two decimal places.]
= Z
b) Calculate the z-score for Hillary's test grade.
[Round your answer to two decimal places.]
= Z
c) Which person did relatively better?
O Emily
O Hillary
O They did equally well.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c270b28-6c5f-463d-8853-d4f8b0737286%2F3cec770e-58d2-4455-a7f3-77b3a638ce5c%2Fd5xucc8_processed.png&w=3840&q=75)
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