posted by Erika Chicas .
If 30% of people in an area registered voters and 15 people are selected at ramdom from this area;
a. What is the probability thatexactly 3out of the15 people are registered voters?
b. What is the probability that at most 3 out of the 15 people are registered voters>
c. could we have used the normal approximation in the binomial in part b? Explain why or why not.
You can use the binomial distribution:
P = nCs*p^s*(1-p)^n(-s) where P is the probability we are hanting for, n = 15 is the size of a sample, s is the number of registered voters of 15 people, and p = 0.3 (30%) is the proportion of registered voters in the area.
a) P(3 of 15) = 15!/(15-3)!3!*(0.3)^3*(1 -0.3)^(15 -3) = 455*0.027*0.01384 = 0.17 or 17%;
b) to get results for "at most 3 of the 15 people", you have to apply the above approach four times:
P(0 of 15) =
P(1 of 15) =
P(2 of 15) =
P(3 of 15) =
then add these four probabilities together => P(at most 3 of 15);
c) I believe that we cannot because the sample of 15 people is too small (the critical size ia about 30 items).