(ii) Using the calculator, we have normal-cdf(0.67,100) = 0.2514. We could get the answer from the
raw data as follows: normalcdf(72,1000,70,3) = 0.2525 , with the difference being due to rounding.
(As explained in the last Calculator Tip, simply add the mean and standard deviation of a nonstandard
normal curve to the list of parameters for normalcdf .)
example: For the population of men in the previous example, how tall must a man be to be in the
top 10% of all men in terms of height?solution: This type of problem has a standard approach. The idea is to express z (^) x in two different
ways (which are, of course, equal since they are different ways of writing the z -score for the
same point): (i) as a numerical value obtained from Table A or from your calculator, and (ii) in
terms of the definition of a z -score.
(i) We are looking for the value of x in the drawing. Look at Table A to find the nearest table entry equal
to 0.90 (because we know an area, we need to read the table from the inside out to the margins). It is
0.8997 and corresponds to a z-score of 1.28.
So zx = 1.28. But also,
So