Statistics Distribution : formula for Z by ClassOf1


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									              Sub: Statistics                                                             Topic: Distribution

              Why the formula for Z used in the following questions.
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              The diameters of oranges in a certain orchard are normally distributed with a mean of 5.26
              inches and a standard deviation of 0.50 inches.
              a. What percentage of the oranges in this orchard has diameters less than 4.5 inches?
              b. What percentage of the oranges in this orchard is larger than 5.12 inches?
              c. A random sample of 100 oranges is gathered and the mean diameter obtained was 5.12. If
              another sample of 100 is taken, what is the probability that its sample mean will be greater
              than 5.12 inches?
              d.Why is the formula for z used in (c) different from that used in (a) and (b)?


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