Quantitative SAT scores are approximately Normally distributed with a mean of 500 and a standard deviation of 100. On the horizontal axis of the graph, indicate the SAT scores that correspond with the provided z-scores. Answer the questions using only your knowledge of the Empirical rule and symmetry. Complete parts a through f. Indicate the SAT scores that correspond with the provided z-scores. Choose the correct answer below. O A. O B. O C. Q Q Q Density Dens Den 21 0 2 2 -3 -2 -1 0 1 2 3 200 300 400 500 600 700 800 -2 -1 0 1 2 3 200 400 500 600 800 1000 0 100 300 500 700 900 1000 a. Roughly what percentage of students earn quantitative SAT scores more than 500? b. Roughly what percentage of students earn quantitative SAT scores between 400 and 600? c. Roughly what percentage of students earn quantitative SAT scores more than 800? d. Roughly what percentage of students earn quantitative SAT scores less than 200? e. Roughly what percentage of students earn quantitative SAT scores between 300 and 700? f. Roughly what percentage of students earn quantitative SAT scores between 700 and 800?The Empirical Rule applies rough approximations to probabilties for any unimodal, symmetric distribution. But for Q the Normal distribution we can be more precise, as the figure shows. Use the figure and the fact that the Normal curve is 68% symmetric to answer the questions. Do not use a Normal Density table or technology. Complete parts a through e. 95% Almost All a. Roughly what percentage of z-scores are between - 2 and 2? b. Roughly what percentage of z-scores are between - 3 and 3? c. Roughly what percentage of z-scores are between - 1 and 1? d. Roughly what percentage of z-scores are more than 0? e. Roughly what percentage of z-scores are between 1 and 2?Eric wants to go skiing tomorrow, but only if there are 4 inches or more of new snow. According to the 0.3- weather report, any amount of new snow between 3 inches and 7 inches is equally likely. The probability 0.2- density curve for tomorrow's new snow depth is shown. Density Find the probability that the new snow depth will be four 0.1- inches or more tomorrow. Copy the graph, shade the appropriate area, and calculate its numerical value to find the probability. The total area is 1. 0 1 2 3 4 5 6 7 8 New Snow Depth (inches) Shade the area of the graph that represents the likelihood of 4 or more inches of new snow. Choose the correct graph below. O A. OB. O c. OD. 0.3- 0.3- 0.2- 0.2- Q 0.2- 0.2- 0.1- 0.1- 0.1- 0 123 4 5 678 01234567 8 01 23 4 5 678 0 1 2 3 45678 What is the probability that there will be 4 or more inches of new snow? (Type an integer or a decimal. Do not round.)K A magician has shaved an edge off one side of a six-sided die, and as a result, the die is no 0.24- longer "fair." The figure shows a graph of the probability 0.2- distribution function (pdf). Show the pdf in table format 0.16- by listing all six possible outcomes and their 0.12 probabilities. 0 08 0.04- Outcome on Die Number of Spots 5 Probability