50. Literacy A researcher reports that 80% of high school graduates, but only 40% of high school dropouts would pass a basic literacy test. Assume that the researcher's claim is true. Suppose we give a basic literacy test to a random sample of 60 high school graduates and an independent random sample of 75 high school dropouts. Let Pg and Pp be the sample proportions of graduates and dropouts, respectively, who pass the test. a. What is the shape of the sampling distribution of Po - Pp? Why? b. Find the mean of the sampling distribution c. Calculate and interpret the standard deviation of the sampling distribution. Verify that the 10% condition is met d. Find the probability that the proportion of graduates who pass the test is at most 0,20 higher than the proportion of dropouts who pass, assuming that the researcher's report is correct.