Question: Family annual expenditure on food and drink( normally distributed), mean=5700, standard deviation=1500
a. What is the range of expenditures of the 10% of the families with the lowest annual expenditure on food and drink?
The 10% is the lowest, so that is on the left side of the distribution. Use =norm.inv(0.1,5700,1500) to give 3777.67. So expenditure would be 3780 (rounding) or less.
b. What percentage of family spend more than $7000 annually on food and drink?
More than means expenditure is greater than $7000. Recall that Excel adds up from the left. So, we will need to subtract from 1. So go =1-norm.dist(7000,5700,1500,true) which gives 0.19. There is a blog posting here
c. What is the range of expenditures for the 5% of families with the highest annual spending on food and drink?
The highest annual expenditure must be on the right of the distribution. It is the little ‘tail’. Recall that Excel adds up from the left. So if you use norm.inv with 0.05, you will get the bottom 5%. So use 0.95, and that will give you the value of the random variable (here annual expenditure) that separates the bottom 95% to the top 5%. Blog posting
=norm.inv(0.95,5700,1500) which gives $8167.28
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