A random sample of 81 eighth gradestudents' scores on a national mathematics assessment test has a mean score of 287. This test result prompts a state school administrator to declare that the mean score for thestate's eighth graders on this exam is more than 280. Assume that the population standard deviation is 35. At =0.02, is there enough evidence to support theadministrator's claim? Complete parts(a) through(e).

Find the standardized test statisticz, and its corresponding area.