A set of final examination grades in an introductory statistics course is normally distributed, with a mean of 79 and a standard deviation of 7. Complete parts (a) through (d). ..... a. What is the probability that a student scored below 91 this exam? The probability that a student scored below 91 is 0.9564 (Round to four decimal places as needed.) b. What is the probability that a student scored between 72 and 99? The probability that a student scored between 72 and 99 is 0.8392 (Round to four decimal places as needed.) c. The probability is 25% that a student taking the test scores higher than what grade? The probability is 25% that a student taking the test scores higher than 84 (Round to the nearest integer as needed.) ion 1 Ist d. If the professor grades on a curve (for example, the professor could give A's to the top 10% of the class, regardless of the score), is a student better off with a grade of 93 on the exam with a mean of 79 and a standard deviation of 7 or a grade of 70 on a different exam, where the mean is 66 and the standard deviation is 47 Show your answer statistically and explain. tion S stion 9 and the Z with a grade of 93 on the exam with mean of 79 and a standard deviation of 7 because the Z value for the grade of 93 is A student is value for the grade of 70 on the different exam is (Round to two decimal places as needed.)
A set of final examination grades in an introductory statistics course is normally distributed, with a mean of 79 and a standard deviation of 7. Complete parts (a) through (d). ..... a. What is the probability that a student scored below 91 this exam? The probability that a student scored below 91 is 0.9564 (Round to four decimal places as needed.) b. What is the probability that a student scored between 72 and 99? The probability that a student scored between 72 and 99 is 0.8392 (Round to four decimal places as needed.) c. The probability is 25% that a student taking the test scores higher than what grade? The probability is 25% that a student taking the test scores higher than 84 (Round to the nearest integer as needed.) ion 1 Ist d. If the professor grades on a curve (for example, the professor could give A's to the top 10% of the class, regardless of the score), is a student better off with a grade of 93 on the exam with a mean of 79 and a standard deviation of 7 or a grade of 70 on a different exam, where the mean is 66 and the standard deviation is 47 Show your answer statistically and explain. tion S stion 9 and the Z with a grade of 93 on the exam with mean of 79 and a standard deviation of 7 because the Z value for the grade of 93 is A student is value for the grade of 70 on the different exam is (Round to two decimal places as needed.)
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Transcribed Image Text:Title: Understanding Normal Distribution in Exam Grades
**Subject Matter: Exam Grade Analysis in Statistics Course**
A set of final examination grades in an introductory statistics course is normally distributed, with a mean of 79 and a standard deviation of 7. Below, we explore several probability scenarios based on this distribution.
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**a. What is the probability that a student scored below 91 on this exam?**
- The probability that a student scored below 91 is **0.9564**.
- (Rounded to four decimal places as needed.)
**b. What is the probability that a student scored between 72 and 99?**
- The probability that a student scored between 72 and 99 is **0.8392**.
- (Rounded to four decimal places as needed.)
**c. The probability is 25% that a student taking the test scores higher than what grade?**
- The probability is 25% that a student taking the test scores higher than **84**.
- (Rounded to the nearest integer as needed.)
**d. Grading on a curve: Statistical Analysis**
If the professor grades on a curve, e.g., giving A's to the top 10% of the class, analyze if a student is better off with:
1. A grade of 93 on the exam with a mean of 79 and a standard deviation of 7.
2. A grade of 70 on a different exam where the mean is 66 and the standard deviation is 4.
Demonstrate your answer statistically and explain.
- **Comparison Criteria:**
- Calculate the Z-score for a grade of 93 with a mean of 79 and standard deviation of 7.
- Calculate the Z-score for a grade of 70 on the alternate exam.
- **Conclusion:**
- This involves entering the Z values into the provided placeholders and rounding the values to two decimal places as needed.
*Note: The Z-score formula is used to determine how far a score is from the mean in terms of standard deviations.*
**Additional Learning Resources:**
- Understand how to calculate probabilities for normally distributed data.
- Learn about Z-scores and their significance in grading curves.
- Apply statistical analysis in real-world grading scenarios.
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For comprehensive understanding, students are encouraged to explore additional resources on normal distribution, Z-scores, and probability calculations in statistics.
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