Suppose that the scores on your next statistics test will be normally distributed with a mean of 66% and a standard deviation of 10%. Using the z-score table find the percentage, and the area under the curve for following a. - d. questions. Draw the standardized normal curve to show your work/calculations. a. A randomly selected student will fall: between 51% and 69% [3 marks] b. What is the probability that a student will score higher than 90% [2 marks] c. What is the probability that a student will score less than 50% [2 marks] d. What is the probability that a student will score between than 50% and 70% [3 marks] e. For a research study purposes for ECON250, the economics department wants to select students in the middle 40% of the population based on an overall score. If the mean score is 66% and the standard deviation is 10%, find the upper and lower scores that would qualify students for this study. [5 marks]