If 75% of all families spend more than $75 weekly for food, while 15% spend more than $150, what is the mean weekly expenditure and what is the standard deviation
Answers
Given : 75% of all families spend more than $75 weekly for food,
while 15% spend more than $150,
To Find : mean weekly expenditure
standard deviation
Solution:
mean weekly expenditure = M
standard deviation = S
Z score = ( Value - Mean) / Standard Deviation
75% of all families spend more than $75 weekly for food
=> Value = 75
Z score for 100 - 75 % = 25 % = 0.25 is -0.675
-0.674 = ( 75 - M )/S
=> M = 75 + 0.674S
15% spend more than $150,
=> Value = 150
Z score for 100 - 15 % = 86 % = 0.85 is 1.036
1.036 = (150 - M )/S
=> M = 150 - 1.036S
75 + 0.674S = 150 - 1.036S
=> 1.71S = 75
=> S = 43.86
M = 104.56
mean weekly expenditure = 104.56 $
standard deviation = 43.86 $
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