SOLUTION: The diameters of grapefruits in a certain orchard are normally distributed with a mean of 6.10 inches and a standard deviation of 0.40 inches. Show all work. (A) What percenta

Question 696933: The diameters of grapefruits in a certain orchard are normally distributed with a mean of 6.10 inches and a standard deviation of 0.40 inches. Show all work.
(A) What percentage of the grapefruits in this orchard have diameters less than 6.8 inches?
(B) What percentage of the grapefruits in this orchard are larger than 6.7 inches?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The diameters of grapefruits in a certain orchard are normally distributed with a mean of 6.10 inches and a standard deviation of 0.40 inches. Show all work.
(A) What percentage of the grapefruits in this orchard have diameters less than 6.8 inches?
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z(6.8) = (6.8-6.1)/0.4 = 0.7/0.4 = 1.75
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P(x < 6.8) = P(z < 1.75) = 0.9599
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(B) What percentage of the grapefruits in this orchard are larger than 6.7 inches?
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z(6.7) = (6.7-6.1)/0.4 = 0.6/0.4 = 3/2
P(x > 6.7) = P(z > 1.5) = normalcdf(1.5,100) = 0.0401
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Cheers,
Stan H.
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