Choose a problem you completed in ALEKS from the "Random Variables & Distributions" pie slice and teach it to me as if I am completely clueless about the concept! Please be specific and state the name of the topic from the pie. Submit the problem, along with the solution, in the discussion thread. You must discuss your thought process and show all work and explanation on how you arrived at the solution. If you do not explain and show the work in its entirety, no credit will be given for the "Content Knowledge" section of the rubric. Remember, you are teaching me the problem so I shouldn't have any questions after you are finished. Do not choose a problem that is ALEKS calculator based. That doesn't teach you anything. PLEASE ANSWER THE BELOW QUESTION, PLEASE EXPLAIN EACH STEP.
Topic: Central limit theorem: Sample Mean
For a standardized psychology examination intended for psychology majors, the historical data show that scores have a mean of 505 and a standard deviation of 175. The grading process of this year's exam has just begun. The average score of the 40 exams graded so far is 512. What is the probability that a sample of 40 exams will have a mean score of 512 or more if the exam scores follow the same distribution as in the past?
Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.