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Evaluation: Solve the following problems. 1. In a given normal distribution, the sample mean is 65 and sample standard deviation is 4. Find the corresponding z-score of a student who receive a score of 55.

Evaluation: Solve the following problems. 1. In a given normal distribution, the sample mean is 65 and sample standard deviation is 4. Find the corresponding z-score of a student who receive a score of 55.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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NOTE: ANSWER THE ACTIVITY BELOW AND PLEASE SKETCH THE NORMAL CURVE
11:35 STAT-Q3-Wk-4-LAS-10-12-TNHS 5 % 0 Q = z = 2 -2 0 2-2-core 88 actual score 70 This indicates that 88 is 2 standard deviation above the mean. Example 3. Mat scored 90 in an English test and 70 in a Physics test. Scores in the English test have a mean of 80 and a standard deviation of 10. Scores in the Physics test have a mean of 60 and a standard deviation of 8. In which subject was his standing better assuming that the scores in his English and Physics class are normally distributed? Solution: For English: For Physics: X-X Z= Z== 70-60 8 z = 1 z = 1.25 His standing in Physics was better than his standing in English. His score in English was one standard deviation above the mean of the scores in English whereas in Physics, his score was 1.25 standard deviation above the mean of the scores in Physics. Example 4: What score marks the 20th percentile of a distribution with a mean of 100 and a standard deviation of 15? Solution: Since we are looking for a raw score, we change the formula for z score into raw score (x). z = becomes x = zs + x Graph the 20th percentile which is equal to the area of 0.2 from the left of the normal curve. Next, look for z-value that marks the 20th percentile. From the table, look for the area that is equal to 0.2. The area is between the z-value 0.84 and 0.85. To determine the z-value, divide this by 2. 0.84 +0.85 z==0.845 z-value x = zs + X x= (0.845) (15)+100 x= 112.675 Evaluation: Solve the following problems. 1. In a given normal distribution, the sample mean is 65 and sample standard deviation is 4. Find the corresponding z-score of a student who receive a score of 55. 2. In a given normal distribution, the population mean is 90 and population standard deviation is 4.5. Find the corresponding z-score of a student who receive a score of 95. 3. On a test in Statistics, the mean is 75 and the standard deviation is 5. Assuming normality, what is the standard score of a student who receives a score of 80? 4. The mean score and the standard deviation in the Statistics test are respectively equal to 80 and 2.5, whereas in the Basic Calculus tests they are respectively equal to 70 and 2. If Genmat got a score of 88 in Statistics and a score of 76 in Basic Calculus, in which subject is his standing better assuming normality in both subjects? Done Solution: z = x-μ a 88-70 9 X-X 90-80 10
Transcribed Image Text:11:35 STAT-Q3-Wk-4-LAS-10-12-TNHS 5 % 0 Q = z = 2 -2 0 2-2-core 88 actual score 70 This indicates that 88 is 2 standard deviation above the mean. Example 3. Mat scored 90 in an English test and 70 in a Physics test. Scores in the English test have a mean of 80 and a standard deviation of 10. Scores in the Physics test have a mean of 60 and a standard deviation of 8. In which subject was his standing better assuming that the scores in his English and Physics class are normally distributed? Solution: For English: For Physics: X-X Z= Z== 70-60 8 z = 1 z = 1.25 His standing in Physics was better than his standing in English. His score in English was one standard deviation above the mean of the scores in English whereas in Physics, his score was 1.25 standard deviation above the mean of the scores in Physics. Example 4: What score marks the 20th percentile of a distribution with a mean of 100 and a standard deviation of 15? Solution: Since we are looking for a raw score, we change the formula for z score into raw score (x). z = becomes x = zs + x Graph the 20th percentile which is equal to the area of 0.2 from the left of the normal curve. Next, look for z-value that marks the 20th percentile. From the table, look for the area that is equal to 0.2. The area is between the z-value 0.84 and 0.85. To determine the z-value, divide this by 2. 0.84 +0.85 z==0.845 z-value x = zs + X x= (0.845) (15)+100 x= 112.675 Evaluation: Solve the following problems. 1. In a given normal distribution, the sample mean is 65 and sample standard deviation is 4. Find the corresponding z-score of a student who receive a score of 55. 2. In a given normal distribution, the population mean is 90 and population standard deviation is 4.5. Find the corresponding z-score of a student who receive a score of 95. 3. On a test in Statistics, the mean is 75 and the standard deviation is 5. Assuming normality, what is the standard score of a student who receives a score of 80? 4. The mean score and the standard deviation in the Statistics test are respectively equal to 80 and 2.5, whereas in the Basic Calculus tests they are respectively equal to 70 and 2. If Genmat got a score of 88 in Statistics and a score of 76 in Basic Calculus, in which subject is his standing better assuming normality in both subjects? Done Solution: z = x-μ a 88-70 9 X-X 90-80 10
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