SOLUTION: 3. The diameters of oranges in a certain orchard are normally distributed with a mean of 6.85 inches and a standard deviation of 0.80 inches. Show all work.
(A) What percent
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Question 309589: 3. The diameters of oranges in a certain orchard are normally distributed with a mean of 6.85 inches and a standard deviation of 0.80 inches. Show all work.
(A) What percentage of the oranges in this orchard have diameters less than 6.3 inches?
(B) What percentage of the oranges in this orchard are larger than 6.7 inches?
(C) A random sample of 100 oranges is gathered and the mean diameter obtained was 6.7. If another sample of 100 is taken, what is the probability that its sample mean will be greater than 6.7 inches?
(D) Why is the z-score used in answering (A), (B), and (C)?
(E) Why is the formula for z used in (C) different from that used in (A) and (B)?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The diameters of oranges in a certain orchard are normally distributed with a mean of 6.85 inches and a standard deviation of 0.80 inches. Show all work.
(A) What percentage of the oranges in this orchard have diameters less than 6.3 inches?
Determine the z-score of 6.3
Find the Prob z is less than that z-score.
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(B) What percentage of the oranges in this orchard are larger than 6.7 inches?
Find the z-score of 6.7 ; then find the probability that z is larger than
that z-score.
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(C) A random sample of 100 oranges is gathered and the mean diameter obtained was 6.7. If another sample of 100 is taken, what is the probability that its sample mean will be greater than 6.7 inches?
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The standard deviation for samples of size 100 is 0.8/sqrt(100) = 0.08
Find the z-value of 6.7 ; then find the prob that z is greater than that
z-value.
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(D) Why is the z-score used in answering (A), (B), and (C)?
Is that obvious or what do they want as an explanation?
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(E) Why is the formula for z used in (C) different from that used in (A) and (B)?
Explained above.
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Cheers,
Stan H.
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