Question 1201215
<font color=black size=3>
Here is the standard normal distribution curve
{{{
drawing(400,400,2,8,4.75,5.5,
line(-5,0,5,0),
graph(400,400,2,8,4.75,5.5,-1000,(1/sqrt(2pi))*e^(-0.5(x-5)^2)+5),

line(-3,5,13,5),line(2,5.02,2,4.98),line(3,5.02,3,4.98),line(4,5.02,4,4.98),line(5,5.02,5,4.98),line(6,5.02,6,4.98),line(7,5.02,7,4.98),line(8,5.02,8,4.98),

locate(1.9,4.95,"-3"),locate(2.9,4.95,"-2"),locate(3.9,4.95,"-1"),locate(4.95,4.95,"0"),locate(5.95,4.95,"1"),locate(6.95,4.95,"2"),locate(7.95,4.95,"3")

)
}}}


We're looking for a value of k such that
P(Z > k) = 0.04

which is indicated in this blue shaded region
{{{
drawing(400,400,2,8,4.75,5.5,
line(-5,0,5,0),
graph(400,400,2,8,4.75,5.5,-1000,(1/sqrt(2pi))*e^(-0.5(x-5)^2)+5),

line(-3,5,13,5),line(2,5.02,2,4.98),line(3,5.02,3,4.98),line(4,5.02,4,4.98),line(5,5.02,5,4.98),line(6,5.02,6,4.98),line(7,5.02,7,4.98),line(8,5.02,8,4.98),

locate(1.9,4.95,"-3"),locate(2.9,4.95,"-2"),locate(3.9,4.95,"-1"),locate(4.95,4.95,"0"),locate(5.95,4.95,"1"),locate(6.95,4.95,"2"),locate(7.95,4.95,"3"),

blue(
line(6.75069,5,6.75069,5.08617),
line(6.75069,5,6.90069,5.06553),line(6.90069,5,7.05069,5.04872),line(7.05069,5,7.20069,5.03542),line(7.20069,5,7.35069,5.02518),line(7.35069,5,7.50069,5.0175),line(7.50069,5,7.65069,5.01189),line(7.65069,5,7.80069,5.0079),line(7.80069,5,7.95069,5.00513),
locate(6.6,5.2,matrix(1,3,area,"=",0.04)),

line(7.1,5.172,7.1,5.07),line(7.1,5.07,7.0482,5.0745),line(7.1,5.07,7.1518,5.0745),

locate(6.75069, 4.995, "k"),
locate(5.75069, 4.8, "P(Z>k)=0.04")
)

)
}}}
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
<a href = "https://davidmlane.com/normal.html">https://davidmlane.com/normal.html</a>
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.


{{{
drawing(400,400,2,8,4.75,5.5,
line(-5,0,5,0),
graph(400,400,2,8,4.75,5.5,-1000,(1/sqrt(2pi))*e^(-0.5(x-5)^2)+5),

line(-3,5,13,5),line(2,5.02,2,4.98),line(3,5.02,3,4.98),line(4,5.02,4,4.98),line(5,5.02,5,4.98),line(6,5.02,6,4.98),line(7,5.02,7,4.98),line(8,5.02,8,4.98),

locate(1.9,4.95,"-3"),locate(2.9,4.95,"-2"),locate(3.9,4.95,"-1"),locate(4.95,4.95,"0"),locate(5.95,4.95,"1"),locate(6.95,4.95,"2"),locate(7.95,4.95,"3"),

blue(
line(6.75069,5,6.75069,5.08617),
line(6.75069,5,6.90069,5.06553),line(6.90069,5,7.05069,5.04872),line(7.05069,5,7.20069,5.03542),line(7.20069,5,7.35069,5.02518),line(7.35069,5,7.50069,5.0175),line(7.50069,5,7.65069,5.01189),line(7.65069,5,7.80069,5.0079),line(7.80069,5,7.95069,5.00513),
locate(6.6,5.2,matrix(1,3,area,"=",0.04)),

line(7.1,5.172,7.1,5.07),line(7.1,5.07,7.0482,5.0745),line(7.1,5.07,7.1518,5.0745),

locate(6.25069, 4.995, "1.751"),
locate(5.25069, 4.8, "P(Z>1.751)=0.04")
)

)
}}}


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 <font color=red>approximately <u>285 grams</u> as the final answer</font>
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