Question

If a data set is approximately normal with sample mean of 75 and sample standard deviation of 5, how many observations fall with 75+ or - 5
(a) 50%
(b) 68%
(c) 95%
(d) 99%

Answer 1

Given : sample mean of 75 and sample standard deviation of 5,

To find :  observations fall with in 75 ±  5

Solution:

Formula to be used

Z =  ( Value - Mean)/Standard Deviation

75 + 5 = 80

=> Z = (80 - 75)/5

=> Z = 1

Data up to Z score 1  = 84.13 %

75 - 5 = 70

=> Z = (70 - 75)/5

=> Z = -1

Data up to Z score -1  = 15.87%

Data between Z - 1 to 1

= 84.13  - 15.87

= 68.26 %

= 68 %

option b is correct

68 % observations fall with in 75 ±  5

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