Supplementary Exercise 1.123 of IPS7e
-------------------------------------

(a) X is the scores of men on the math SAT
    X follows N(537, 116). Z follows N(0,1). 

Standardization + table/computer lookup, in condensed notation:
P(X>750) = 1-P(X<750) = 1-P((X-537)/116 < (750-537)/116) 
         = 1-P(Z<1.8362) = 1-0.9668 = 0.033 = 3.3%


(b) X is the scores of women on the math SAT
    X follows N(503, 110). Z follows N(0,1). 

Standardization + table/computer lookup, in condensed notation:
P(X>750) = 1-P(X<750) = 1-P((X-503)/110 < (750-503)/110) 
         = 1-P(Z<2.2455) = 1-0.9876 = 0.012 = 1.2%


It is seen that the probabibility dropped down to almost one third
between the two settings, with moderately small changes in mean 
(relatively to the standard deviations) and standard deviations. 
In this case, the change in standard deviations affects the probability 
in the same way as the change in the means: both lead to larger z-scores
and hence a smaller probability.

---

Minitab commands and output:

 CDF 750;
  Normal 537 116.
--
Normal with mean = 537 and standard deviation = 116

  x  P( X <= x )
750     0.966836
--

 CDF 750;
  Normal 503 110.
--
Normal with mean = 503 and standard deviation = 110

  x  P( X <= x )
750     0.987631
--