(1) Calculate the Z value for the AQI at 100, given an average of 90 and standard deviation of 8. Do this calculation in cell C3. (2) What is the probability that a given day has an AQI over 100? Do this calculation in call C6. (3) In a 365-day year, what is the expected number of days of AQI over 100? Do this calculation in cell C8. Do not round your result. (4) Simulate 1000 days of AQI readings based on the following instructions: (a) in cells F3-F1002, generate a random number between 0 and 1, using the RAND function in Excel; (b) in cells G3-G1002, generate an AQI at random using the NORMINV function in Excel (and remember that the average of the distribution is 90 and the standard deviation is 8). After you complete this exercise, you need to copy all numbers and use paste them in the same locations using the Paste Values feature. (Note that although this will not be directly graded, it needs to be done correctly to provide a reasonable-looking graph that is described below. (5) In your sample in cells G3-G1002, calculate in cell G1005 the number of days of AQI over 100, using the COUNTIF function in Excel. (6) Graph 1: Create a histogram of the simulated AQI readings in cells G3-G1002. To get credit, you must have an appropriate title for the graph, you must set the bin width on the horizontal axis to 5, the entire range of each bin must be visible (make the graph larger if needed), and the distribution must look approximately normal with a peak close to 90. (Note: If you do not have a normal-looking distribution, you need to repeat elements 4-6.)