The diametersof oranges in a certain orchard are normally distributed with amean

Question

The diametersof oranges in a certain orchard are normally distributed with amean of 7.25 inches and a standard deviation of 0.75 inches. Show all work.

(A) What percentage of theoranges in this orchard have diameters less than 6.5inches?

(B) What percentage of theoranges in this orchard are larger than 7.1 inches?

(C) A random sample of 100oranges is gathered and the mean diameter obtained was 7.1. Ifanother sample of 100 is taken, what is the probability that itssample mean will be greater than 7.1 inches?

(D) Why is the z-score used inanswering (A), (B), and (C)?

(E) Why is the formula for zused in (C) different from that used in (A) and(B)?

Explanation / Answer

Given X~Normal(=7.25, =0.75) (a)P(X-0.2) = 0.5792 (check normal table) (c) n=100 P(Xbar > 7.1) = P((xbar-)/(/n) >(7.1-7.25)/(0.75/sqrt(100))) =P(Z>-2) = 0.9772 (check normal table) (d) becuase the diameters of oranges are normally distribution. (e) In (c) is calculated by the sample mean.

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