Please help with this math?

Question

In June 2003, approximately 45% of a workforce were women. In a random sample of 20 workers:a) What is the probability that six are women?b) What is the probability that there were 12 or more men?Please help Thanks in advance. ?

Answer 1

The binomial distribution gives the discrete probability distribution  of obtaining exactly  successes out of  Bernoulli trials (where the result of each Bernoulli trial is true with probability  and false with probability ). The binomial distribution is therefore given by

   (1)  nCr p^(n) q^(n-r)

    

where nCr is a binomial coefficient.

  

n = 20,  p = .45 (probability being women)  q = 0.55 (probability being men)

exact 6 women  

                             20C6 ( 0.45)^6 (0.55)^(20-6)

12 or more men

sum of 12+13+  .....  20 men

         12           20C12 ( 0.55)^12 (0.45)^(20-12)

         13           20C13 ( 0.55)^13 (0.45)^(20-13)

        14, 15,16,17,18,19,20