Exercise 1: Solving for X In 2021, the average SAT score for students in the freshman class of Nunya Business College was 1025 with a standard deviation of 100. Solve for X using z-values obtained from Microsoft Excel and the Area Under the Cu Table. Population Mean, µ, = 1,025 Population Standard Deviation, 6, 100 X = µ + zo You can find the z-values using either of the two z-values tables or by using the formula found in the assignmen and on the Excel file 09_SolvingforX.xlsx. The Excel function for finding the preproperate z-value is: = NORM.S.INV(Probability) When using Excel, please noted that the Area on the Curve starts from the left of the curve. Excel finds the z-val differently that the Area Under the Curve table. The Area Under the Curve table starts and the mean, which is th center of the curve. And, it only covers the right side of the normal curve, which means that all z-values on this t are positive. But, because the normal curve is symmetrical, z-values on the left side of the curve will be negative The probabilities, however, are always positive. So, the z-value for the lowest 1% will be -2.33 (using the Area Under the Curve Table) and 2.33 for the highest 1%. To find the z-value for the lowest 1%, the formula for Exce would be NORM.S.INC(0.01) while the formula for the top 1% would be =NORM.S.INV(0.99). Note: Given that SAT scores are reported as whole numbers round off your answer for X to a whole num The z-values found using Excel are rounded off to the thousandths place, which is three decimal places to right of the decimal point. When using the Area Under the Curve table, z-values are reported with two dis places passed the decimal point. Using Excel or the Table, the value for X should be very close. The values found using Excel are more precise. 1. What SAT score do you need to be among the top 0.5 percent? z = NORM.S.INV(?) z w/Excel Z-value 1,025 1,064 100 100 Area Under the Curve Table 2. What SAT score do you need to be among the top 2.5 percent? z= NORM.S.INV(?) z w/Excel X Z-value 1,025 1,064 100 100 Area Under the Curve Table 3. What z-value is the cut-off point for the bottom 10 percent? z = NORM.S.INV(?) z w/Excel X Z-value 1,025 1,064 100 100 Area Under the Curve Table 4. What z-value is the cut-off point for the bottom 1 percent? z = NORM.S.INV(?) z w/Excel X Z-value 1,025 100 1,064 100 Area Under the Curve Table