11 Find the standard deviation of the binomial distribution

11) Find the standard deviation of the binomial distribution for which n = 1000 and p = 0. 12) Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Find the probability of exactly nine boys in ten births.

Solution

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    10      
p = the probability of a success =    0.5      
x = the number of successes =    9      
          
Thus, the probability is          
          
P (    9   ) =    0.009765625 [answer]