Explanation Given info: Mean of test scores, μ = 100 Standard deviation, σ = 20 Concept used: 68 − 95 − 99.7 Rule:- It implies that 68 % of test scores falls within 1 − standard deviation of mean. 95 % Of test scores fall within 2 − standard deviation. 99.7 % fall within 3 − standard deviation of mean. Calculation: (a)For data to be normally distributed and symmetric about mean, half of the value will fall below the mean and half above the mean. Therefore, 50 % of the scores will be less than 100 (b)Since, mean of test score is given which is equal to 100 and standard deviation is equal to 20 . By using one standard deviation of mean ( μ ± σ ) , value of 120 can be obtained. By applying 68 − 95 − 99.7 rule, 68 % of test scores fall within the 1 − standard deviation of mean. Now, μ ± σ = 100 ± 20 = 80 , 120 That means, 68 % of test score will lie in the interval ( 80 , 120 ) .Remaining 32 % falls outside the interval ( 80 , 120 ) .Since, Normal distribution is symmetric about mean then 16 % will fall less than score 80 and 16 % fall more than score 120 Therefore, total percentage of score that is less than 120 is 84 % (c)Score of 140 can be obtained using two standard deviation of mean ( μ ± 2 σ ) By applying 68 − 95 − 99.7 rule, 95 % of test scores fall within the 2 − standard deviation of mean. Now, μ ± 2 σ = 100 ± 40 = 60 , 140 That means, 95 % of test score data will lie in the interval ( 60 , 140 ) .Since, Normal distribution is symmetric about mean thus remaining 5 % will fall outside this range. 2.5 % Below the test score of 60 And 2.5 % above the test score of 140 .

6th Edition

ISBN: 9780137721023

Author: Bennett

Publisher: PEARSON C

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Chapter 6.C, Problem 19E

To determine

The percentage of scores in each of the following categories.

(a)Less than $100$ (b) Less than $120$ (c) Less than $140$ (d) Less than $60$

(e)Greater than $60$ (f) Greater than $160$ (g) Greater than $80$ (h) Between $60$ and $140$

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Chapter 6.C, Problem 18E

Chapter 6.C, Problem 20E

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The percentage of scores in each of the following categories. (a)Less than 100 (b) Less than 120 (c) Less than 140 (d) Less than 60 (e)Greater than 60 (f) Greater than 160 (g) Greater than 80 (h) Between 60 and 140