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Q. Find Probabilities for the Standard Normal Distribution?
Ans.
Suppose the history teacher decides to distribute the final grades of his class with a normal distribution. He wants to give a score of C or higher to all students who score within 1.1 standard deviations of the mean. What percentage of students will receive a mark of C or greater?
Solution:
Use the table of probabilities for the normal standard distribution. The table shows that . This means that 86.43% of students have a z-score less than 1.1.
We know that 50% of the students scored below the mean. Thus, 86.43% or 50% = 36.43% of the students scored between the mean and 1.1 standard deviations above it.
Since the normal distribution is symmetric, there is also 36.43% of students which scored between a z-score of 1.3 and the mean.
The total percentage of students within 1.1 standard deviations of the mean is .
Thus 72.86% of the students in the history class will get a final mark of C or higher.
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