Question

Suppose that Fred, a United States politician from a large western state, wants to create a new law that would require children under the age of 16 to be accompanied by an adult at all times in public places. Based on previous voting records, Fred believes that he could gain the support of 25% of likely voters. To test his hypothesis, Fred conducts a random survey of 1200 likely voters and asks if they would support his proposition. Let X denote the number of likely voters in Fred's sample that pledge their support . Which of the following statements are true about the sampling distribution of X? O The sampling distribution of X is exactly normal with u = 0.5 and a = 0.0125. " The sampling distribution of X is exactly binomial with in = 1200 and p = 0.25. O The sampling distribution of X is exactly normal with u = 300 and a = 15. 0 The sampling distribution of X is approximately normal with a = 0.5 and o = 0.0125. 0 The sampling distribution of X is approximately normal with u = 300 and os = 15. O The sampling distribution of X is approximately binomial with n = 1200 and p = .. 25

Answer 1

Answer:

The sampling distribution of X is exactly binomial with n = 1200 and p = 0.25

Step-by-step explanation:

For each person surveyed, there are only two possible outcomes. Eithey they support his proposition, or they do not support his proposition. So the sampling distribution of X is exactly binomial.

Binomial probability:

Probability of exactly x sucesses on n repeated trials, with a p probability.

He surveyes 1200 likely voters, so $n = 1200$

He believes he could gain the support of 25% of likely voters. So $p = 0.25$.

The correct answer is:

The sampling distribution of X is exactly binomial with n = 1200 and p = 0.25