Question 1:
Over 90% of the nation's school districts, according to a recent research published in the Journal of Education, reported that their students were scoring "above the national average" on standardized tests. Using your knowledge of measures of central tendency, explain why the schools' reports are incorrect. Does your analysis change if the term "average" refers to the mean? To the median? Explain what effect this misinformation might have on the perception of the nation's schools.
Question 2:
Simran can either take a course in Math or in Biology, if Simran takes the math course, then she will receive an A grade with probability 1/5. If she takes the Biology course she will receive an A grade with probability 1/6. Simran decides to base her decision on the flip of a fair coin. What is the probability that Simran will not get an A in Math?
Question 3:
There is a 50-50 chance that the king carries the gene of twins. If he is a carrier, then each princess has a 50-50 chance of having twins independently. If the king is not a carrier, the princess will not have the disease. Suppose the king has had three princeses without the disease. What is the probability the king is a carrier?
Question 4:
The final grades given by two professors in introduction to Sociology course have been carefully examined. The students in the first professor's class had a grade point average of 5.0 and a standard deviation of 0.4. Those in the second professor's class had grade points with an average of 5.0 and a standard deviation of 2.0. If you had a choice, which professor would you take for this course?
Question 5:
Suppose that N balls are labelled 1,2,...,N are placed in a box, and n balls (N are randomly selected without replacement. Define the r.v.
X=Largest number selected.
Find the probability function for X.