Suppose 30% of the U. S. population has green eyes. If a random sample of size 1200 U. S. citizens is drawn, then the probability that less than 348 U. S. citizens have green eyes is .

P(X is less than 348) = 0.2148

Step-by-step explanation:

Given that:

Sample proportion (p) = 0.3

Sample size = 1200

Let X be the random variable that obeys a binomial distribution. Then;

The Binomial can be approximated to normal with:

To find:

P(X< 348)

So far we are approximating a discrete Binomial distribution using the continuous normal distribution. 348 lies between 347.5 and 348.5

Normal distribution:

x = 347.5, = 360, = 15.875

Using the z test statistics;

z = -0.7874

z ≅ - 0.79

The p-value for P(X<347.5) = P(Z < -0.79)

From the z tables;

P(X<347.5) = 0.2148

Thus;

P(X is less than 348) = 0.2148

good for u

step-by-step explanation:

1/800 is the right answer