Question

An organization claims that 39.2% of all Americans approve of candidate A. In a random sample of 100 Americans approximate the probability that at least 35 people will approve of candidate A.

Answer 1

Here we have

n=100 and p=0.392

Since np = 39.2 and n(1-p) = 60.8 both are greater than 5 so we can use normal approximation here.

Using normal approximation, X has approximately normal distribution with mean and SD as follows:

The z-score for X = 35-0.5 = 34.5 is

The  probability that at least 35 people will approve of candidate A is

P(X >= 35) = P(X > 34.5) = P(z > -0.96) = 1 - P(z <= -0.96) = 0.8315

Answer: 0.8315