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Calculus/MS-08: Quantitative Analysis for Managerial Applications

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Expert: - 10/6/2010


Question
3.   From a set of 1000 observations known to be normally distributed, the mean is 534 cm and SD is 13.5 cm.  How many observations are likely to exceed 561 cm? How many will be between 520.5 cm and 547.5 cm? Between what limits will the middle 50% of the observations lie?

Answer
Use the normal table
mathsisfun.com/data/standard-normal-distribution-table.html
the number between 0 and z can be found.

Take (561 - 534)/13.5 and look it up on a normal table.
It looks like it should be 2.  To do this, find the P(0<z<2).

The result to look up are how many are greater than this many SD.

For 520.5 to 547.5, find out how many are between (it looks like)
-1 and 1 on the normal standard deviatiom table.  This is the same as 2p(0<z<1).

To find out where 50% would lie, that would be 25% over 0 and 25% less than 0 on a normal distribution table.

After looking at the table, that would be roughly betwen u-0.675s
and u+0.675s.  The value for u is the average and for s is the standard deviation.

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