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The value for μ is 1,025. It is not 1,064

The value for μ is 1,025. It is not 1,064

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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The value for μ is 1,025. It is not 1,064
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 Curve Table. Population Mean, µ, = 1,025 Population Standard Deviation, o, 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 assignment 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-value differently that the Area Under the Curve table. The Area Under the Curve table starts and the mean, which is the center of the curve. And, it only covers the right side of the normal curve, which means that all z-values on this table 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 Excel 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 number. The z-values found using Excel are rounded off to the thousandths place, which is three decimal places to the right of the decimal point. When using the Area Under the Curve table, z-values are reported with two digit 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. What SAT score do you need to be among the top 0.5 percent? 1. 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 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 Z-value 1,025 100 1,064 100 Area Under the Curve Table
Transcribed Image Text: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 Curve Table. Population Mean, µ, = 1,025 Population Standard Deviation, o, 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 assignment 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-value differently that the Area Under the Curve table. The Area Under the Curve table starts and the mean, which is the center of the curve. And, it only covers the right side of the normal curve, which means that all z-values on this table 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 Excel 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 number. The z-values found using Excel are rounded off to the thousandths place, which is three decimal places to the right of the decimal point. When using the Area Under the Curve table, z-values are reported with two digit 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. What SAT score do you need to be among the top 0.5 percent? 1. 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 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 Z-value 1,025 100 1,064 100 Area Under the Curve Table
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