Question 458426: Suppose the distribution of the diameter (in cm) of oranges from a tree is N(10,2^2) ..
a. Sketch a graph of the distribution that displays both the actual diameters as well as the z-score along the horizontal axis.
b. Find the z-score for each of the following diameters :
a) 12 cm b)9 mm c)13 cm
c. Oranges are to be dumped if their diameters have a z-score of less than -2.
what is the diameter of oranges that are to be dumped?
d If there are 120 oranges on the tree how many will be dumped?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Suppose the distribution of the diameter (in cm) of oranges from a tree is
N(10,2^2) ..
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a. Sketch a graph of the distribution that displays both the actual diameters as well as the z-score along the horizontal axis.
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b. Find the z-score for each of the following diameters :
a)12 cm::: z = (12-10)/4 = 1/2
b)9 mm ::: z = (9-10)/4 = -1/4
c)13 cm::: z = (13-10)/4 = 3/4
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Note: If the 9mm is really 9mm and not a typo,
9/1000 = 90/100 = 90cm
In which case the z-value is (90-10)/4 = 80/4 = 20
c. Oranges are to be dumped if their diameters have a z-score of less than -2.
what is the diameter of oranges that are to be dumped?
Use x = zs+u
x = -2*4+10 = 2 inches
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d If there are 120 oranges on the tree how many will be dumped?
P(z < -2) = normalcdf(-100,-2) = 0.02275
# to be dumped = 0.02275*120 = 2.73 ~ 3 when rounded up
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Cheers,
Stan H.
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