The statistics teacher was surprised that 42% of the students in the sample had a failing grade (<60%). They wondered if this value was unusual, so they simulated 100 samples of size 50. The sampling distribution of the sample mean is shown below. 1. Based on this distribution is a value of 42% of students not passing unusual? Explain.
2. A student from the statistics class wants to know what the probability of getting a C (70%) or higher is. Use the sampling distribution from the last question whereμx= 60.523 and σ x= 2.97 to help calculate your answer. Be sure to show all of your work to earn credit.
3. Based on the original sample mean, standard deviation, and sample size from the original set (#1), construct and interpret (4-step process) a 95% confidence interval for the true mean score of all students who take this test.