The average daily sales of 500 branch office were Rs .150thousands and the standard Deviation Rs. 15 thousands Assuming the distribution to be normal indicate how manu branch have sales between 1. Rs. 120thousands and Rs 145 thoudands (z values=0.4772 and 0.1293) 2. Rs. 140thousands and Rs. 165 thousands (z values=0.2486 and 0. 3413)
Answers
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Given : The average daily sales of 500 branch office were Rs .150thousands and the standard Deviation Rs. 15 thousands distribution to be normal indicate
To Find : how many branch have sales between
1. Rs. 120thousands and Rs 145 thoudands (z values=0.4772 and 0.1293)
2. Rs. 140thousands and Rs. 165 thousands (z values=0.2486 and 0. 3413)
Solution:
(z values mentioned in Question are with taking Mean = 0 and on right side are + ve and left side are - ve ) hence from - 0.50 to 0.50
( these values are always confusing Hence )
Here I have used Z values from 0 to 1
Z score = (Value - Mean)/SD
Mean = 150 thousands
SD = 15 thousands
Rs. 120thousands and Rs 145 thoudands
Z score for 120
= (120 - 150)/15 = - 2 => 2.28 %
Z score for 145
= (145 - 150)/15 = - 1/3 => 37.07 %
Between = 37.07 - 2.28 = 34.79 %
34.79 % of 500
= 173.95 People
= 174 People
Rs. 140thousands and Rs 165 thoudands
Z score for 120
= (140 - 150)/15 = - 2/3 => 25.14 %
Z score for 165
= (165 - 150)/15 = 1 => 84.13 %
Between =84.13 - 25.14 = 58.99 %
58.99 % of 500
= 294.95 People
= 295 People
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