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Hi, Could you please help me understand why we are looking at 0.975 for 95%? Shouldn't 0.975 be for 97.5%? Thank you

Hi, Could you please help me understand why we are looking at 0.975 for 95%? Shouldn't 0.975 be for 97.5%? Thank you

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 22PFA
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Hi,

Could you please help me understand why we are looking at 0.975 for 95%? Shouldn't 0.975 be for 97.5%?

Thank you

To determine To obtain: The positive z-score for which 95% of the distribution's area lies between -z and z. Answer to Problem 1TY The positive z-score for which 95% of the distribution's area lies between -z and z is 1.96. Explanation of Solution Calculation: The positive z-score for 95% of the distribution's area lies between -z and z represents the cumulative area of 0.975 to the left of z-score and the cumulative area of 0.025 to the right of z-score. Shade the cumulative area of 0.975 to the left of z-score as shown in Figure (1). Area = 0.975 z Figure (1) Use Table 4: Standard normal distribution to find the z-scores. Procedure: • Locate an approximate area of 0.975 in the body of the Table 4. • Move left until the first column and note the values as 1.9. • Move upward until the top row is reached and note the value as 0.06. Thus, the positive z-score for which 95% of the distribution's area lies between -z and z is 1.96.
Transcribed Image Text:To determine To obtain: The positive z-score for which 95% of the distribution's area lies between -z and z. Answer to Problem 1TY The positive z-score for which 95% of the distribution's area lies between -z and z is 1.96. Explanation of Solution Calculation: The positive z-score for 95% of the distribution's area lies between -z and z represents the cumulative area of 0.975 to the left of z-score and the cumulative area of 0.025 to the right of z-score. Shade the cumulative area of 0.975 to the left of z-score as shown in Figure (1). Area = 0.975 z Figure (1) Use Table 4: Standard normal distribution to find the z-scores. Procedure: • Locate an approximate area of 0.975 in the body of the Table 4. • Move left until the first column and note the values as 1.9. • Move upward until the top row is reached and note the value as 0.06. Thus, the positive z-score for which 95% of the distribution's area lies between -z and z is 1.96.
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