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the annual per capita consumption of fresh apples (in pounds) in the united states
can be approximated by a normal distribution with a mean of 16.2 pounds
and a standard deviation of 4 pounds
(a) what is the smallest annual per capita consumption of apples can be in the top 25% pf consumption?
(b) what is the largest annual per capita consumption of apples that can be in the bottom 15%
of consumption?
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To solve this problem, forget about apples and concentrate on the given normal curve.
Each normal curve is a bell shaped.
In part (a), they want you find the highest raw score z such that the area on the right
of this z-score is 0.25 (and, hence, the area on the left of this z-score is 1-0.25 = 0.75).
To find this raw score z, use the function invNorm, which is the inverse function
to the cumulative normal distribution function.
This function invNorm is in your calculator TI-83/84.
Its format is z = invNorm(area, mean, SD).
In your problem, the input for the calculator function is
area = 0.75 = 1-0.25; the mean value and SD are given.
So, you print in your calculator invNorm(0.75, 16.2, 4),
and you get the answer z= 18.898 pounds, which you can round to z = 19 pounds.
For instructions on how to get this function invNorm in your calculator, if you need them,
see this web-page https://www.statology.org/invnorm-ti-84/
If you are a beginner student in such calculations, I recommend you to go to web-site
https://davidmlane.com/hyperstat/z_table.html.
Find there free of charge online calculator, specially created for such problems.
It has perfect design, so any beginner student can work with it on his or her own
without help from outside.
For your problem, use the mode "value from the area"
and look for the answer in the window "Below".
The calculator will show you the area of interest as shaded, so you will understand
everything that you are doing and what the calculator does for you.
This calculator is the best tool for the beginners to learn the subject.
For part (b), the same /(or similar) mantra does work.
In part (b), they want you find the highest raw score z such that the area on the left
of this z-score is 0.15. Notice that this time the area of interest is on the left side
of the z-score.
Again, use the standard function invNorm, now in this format
area mean SD <<<---=== formatting pattern
z = invNorm(0.15, 16.4, 4)
Your answer should be z= 12.054 pounds, which you can round to z= 12 pounds.
For part (b), the same recommendation works regarding the online calculator.
Solved.
