4 If 30 of people in an area are registered voters and 15 pe

4. If 30% of people in an area are registered voters and 15 people are selected at random from this area: a. [4 points] What is the probability that exactly 3 out of the 15 people arc registered voters? b. [5 points] What is the probability that at most 3 out of the 15 people are registered voters? c. [3 points] Could we have used the normal approximation to the binomial in part b? Explain why or why not.

Solution

Total 30% people are registered.

Selected 15 at random.

X no of voters registered follow a Binomial with p = 0.3 and n =15

Hence required prob = P(X=3) = 15C3(0.3)³(0.7)¹²