Suppose a professor uses a normal distribution to assign grades in her math class. She assigns an A to students scoring more than 1.8 standard deviations above the mean. She assigns an F to students scoring more than 2.2 standard deviations below the mean. She assigns a B to students who score between 1.1 and 1.8 standard deviations above the mean. She assigns a D to students who score between 0.8 and 2.2 standard deviations below the mean. All other students get a C. Use the Cumulative Z-Score Table to answer the following questions. The Z-Score Table can be found below by selecting "Read". Write your answer as a percent using 2 decimal places. What percent of the class receives each grade assuming the scores are normally distributed?
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.
Suppose a professor uses a normal distribution to assign grades in her math class.
- She assigns an A to students scoring more than 1.8 standard deviations above the mean.
- She assigns an F to students scoring more than 2.2 standard deviations below the mean.
- She assigns a B to students who score between 1.1 and 1.8 standard deviations above the mean.
- She assigns a D to students who score between 0.8 and 2.2 standard deviations below the mean.
- All other students get a C.
Use the Cumulative Z-Score Table to answer the following questions. The Z-Score Table can be found below by selecting "Read".
Write your answer as a percent using 2 decimal places.
What percent of the class receives each grade assuming the scores are
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