Question

1.A jury of 12 people is to be randomly selected from a group of 30 people (18 women and 12 men).  Let the random variable X = “number of women on the jury of 12.”  Find (using R):

      

      a) P(X = 6)

      b) P(X ≤ 8)

      c) P(5 ≤ X ≤ 10)

      d) P(no men on the jury)

Answer 1

Since , X =“number of women on the jury of 12.” follows Binomial distribution ie Bin ( n,p)

where n = 12 and p = 18/30 ie p= 0.6. X is Binomial since there can be only 2 outcomes of an event ( women selected or not selected). Also, the trials are independent of each other.

Attached please find the R Code :