According to national data, about 15% of American college students earn a graduate degree. Using the estimate, what is the probability that exactly 26 undergraduates in a random sample of 200 students will earn a college degree?

1. What is the population mean ()?
2. What is the population variance ?
3. Sketch the distribution of this population. Make sure you draw the shape of the distribution and include the mean plus and minus three standard deviations
4. What is the mean of the sampling distribution for samples of size 4 from this population? Note: The mean of the sampling distribution is .
5. What is the standard error for this sampling distribution? Note: The standard error of the sampling distribution is
6. Based on your calculations for the mean and standard error, sketch the sampling distribution of the mean taken from this population. Make sure you draw the shape of the distribution and include the mean plus and minus three standard errors.
7. If a researcher takes one sample of size 4 (n = 4) from this population, what is the probability that he or she computes a sample mean of at least 23 (M = 23) minutes? Note: You must compute the z-transformation for sampling distributions, and then refer to the unit normal table to find the answer.
8. Now say a researcher decides to take a sample of size 36 (n = 36) and calculates the same sample mean (M = 23).
   1. Compute the mean and standard error for this new sampling distribution. Sketch the sampling distribution taken from this same population. Make sure you draw the shape of the distribution and include the mean plus and minus three standard errors. Hint: A larger sample size will decrease the standard error of the mean.
   2. Now what is the probability of obtaining at least this sample mean of 23 minutes when n = 36?
9. From which sample (n = 4 or n = 36) is there a lower probability of collecting a sample mean of 23 from a population with a mean of 20?
10. What does your answer to question 9 indicate about the relationship between sample size and standard error?