<PRE><B>Question 1138943</B>
Use the Binomial Probability Formula,
:
Probability(P) (k successes in n trials) = nCk * p^k * (1-p)^(n-k), where nCk = n!/(k! * (n-k)!), p is probability of one success
:
For this problem p = 16/64 = 0.25, n = 1000
:
3.2.1 P(at most 375 will be female) = summation for k from 0 to 375 of 1000Ck * (1/4)^k * (1-(1/4))^(1000-k) = 0.999999 
:
3.2.2 P(at least 420 of them will be female) = summation for k from 420 to 1000 of 1000Ck * (1/4)^k * (1-(1/4))^(1000-k) = 0.000001 
:
 </PRE>