SOLUTION: A particular fruit's weights are normally distributed with a mean of 250 grams and a standard deviation of 20 grams. The heaviest 4% of fruits weigh more than how many grams. Round

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Question 1201215: A particular fruit's weights are normally distributed with a mean of 250 grams and a standard deviation of 20 grams. The heaviest 4% of fruits weigh more than how many grams. Round your answer to the nearest gram.
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52777) About Me  (Show Source):
You can put this solution on YOUR website!
.
A particular fruit's weights are normally distributed with a mean of 250 grams
and a standard deviation of 20 grams. The heaviest 4% of fruits weigh more than
how many grams. Round your answer to the nearest gram.
~~~~~~~~~~~~~~~~~~~ 

From the curve of the normal distribution with the mean of 250 grams and 
the standard deviation of 20 grams, we should find z-score in a way, 
that the area under the curve on the right of the z-score would be 4%.


So, go to website

https://davidmlane.com/hyperstat/z_table.html

and use free of charge online calculator, specially developed for such tasks.

    (Use it in the mode "Value from an area").


In the calculator ports, assign these input parameters

    Area 0.04

    Mean  250

    SD      4


    Option: Above.


Then press "Recalculate" button  and get the number 285 grams  (rounded to the nearest gram).


It is the answer to the problem's question.


Alternatively, you may use the standard function invNorm in your regular calculator TI-84

                prob.  mean SD    <<<---===  formatting pattern
    P = invNorm(0.96,  250, 20).


You will get the same answer  P = 285 grams  (rounded to the nearest gram).

Solved.



Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

Here is the standard normal distribution curve


We're looking for a value of k such that
P(Z > k) = 0.04
which is indicated in this blue shaded region

It's the region to the right of z = k.
The blue region has an area of 0.04

Fruits in this blue region correspond to the top 4% in terms of weight (i.e. the heaviest 4%)

Use a calculator like this one
https://davidmlane.com/normal.html
or a TI83/TI84 to find the value of k is roughly k = 1.751
Use of a Z table is another option.

Therefore, P(Z > 1.751) = 0.04 approximately.



We'll use this approximate value as the z score to find the raw score x.
z = (x-mu)/sigma
1.751 = (x-250)/20
1.751*20 = x-250
35.02 = x-250
x = 35.02+250
x = 285.02
Rounding to the nearest gram gets us approximately 285 grams as the final answer