A growth-mindset researcher plans to take an SRS of 200 teenagers from the population of teenagers in North America to see what proportion of teenagers sampled are pursuing a goal they have set for themselves. Suppose that 75% of teenagers in North America are pursuing a goal they have set for themselves. Let p represent the proportion of a sample of 200 teenagers in North America who are pursuing a goal they have set for themselves. What are the mean and standard deviation of the sampling distribution of p?

The mean of the sampling distribution of p is 0.75 and the standard deviation is 0.0306.

Step-by-step explanation:

Central Limit Theorem:

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation

75% of teenagers in North America are pursuing a goal they have set for themselves.

This means that

Sample of 200.

This means that .

What are the mean and standard deviation of the sampling distribution of p?

By the Central Limit Theorem

Mean

Standard deviation

The mean of the sampling distribution of p is 0.75 and the standard deviation is 0.0306.

The height of the tower is given by