Explain why the Z score used for the subsequent data.
The diameters of oranges in a definite orchard are usually distributed with a mean of 5.26 inches and a standard deviation of 0.50 inches.
1) What percentage of the oranges in this orchard have diameters less than 4.5 inches?
2) What percentage of the oranges in this orchard is larger than 5.12 inches?
3) A random sample of 100 oranges is gathered and the mean diameter obtained was 5.12. If additional sample of 100 is taken then what is the probability that its sample mean will be greater than 5.12 inches?
4) Why is the z-score used in answering (a), (b), and (c)?
5) Why is the formula for z used in (c) different from that used in (a) and (b)?