Binomial Distribution

Question

A box contains the 120 numbers, of which 48 are negative (less than zero), 60 between 0 and 10, with the remaining 12 being bigger than 10. We will make 64 draws from this box, one at a time, possibly with or without replacement. Thus, we will obtain a SRS of size 64. Let the random variable X be the COUNT of negative numbers among the 64 sampled. Let Y be the COUNT of numbers bigger than 10 among the 64 sampled.

1. Refer to exhibit 1. Consider the draws to be made with replacement. What is the probability that X = 47?

Answer 1

In one draw the prob that a draw is negative is 48/120 = 2/5.  Thus the prob that a draw is not negative = 3/5

 

The formula would be 

 

120 C X * (2/5)^X*(3/5)^(120-X)

120 C 47*(2/5)^47*(3/5)^73  =  .07316