Question

2. Suppose it is known that 37% of people in a certain city support Candidate Y for

mayor. You randomly select 8 people from this city. Let z be the number of people in
your sample that support Candidate Y for mayor.
find the probability that x is less then or equal to 2

Answer 1

To find the probability that x is less than or equal to 2, we use the binomial probability formula. The probability of supporting Candidate Y is 37%. Plugging in the values, we get a probability of 0.439.

Step-by-step explanation:

To find the probability that x is less than or equal to 2, we need to use the binomial probability formula. We know that the probability of supporting Candidate Y is 37% or 0.37. The formula is P(X <= 2) = P(X=0) + P(X=1) + P(X=2).

Using the binomial probability formula, P(X=k) = C(n,k) * p^k * (1-p)^(n-k), where n is the sample size, p is the probability of success, and k is the number of successes. In this case, n=8, p=0.37.

Plugging in the values, we have P(X <= 2) = C(8,0) * 0.37^0 * (1-0.37)^(8-0) + C(8,1) * 0.37^1 * (1-0.37)^(8-1) + C(8,2) * 0.37^2 * (1-0.37)^(8-2).

Calculating the values, we get P(X <= 2) = 0.025 + 0.131 + 0.283 = 0.439.