Normal Distribution Calculations Backward Section 2 2 Finding

Normal Distribution Calculations (Backward) Section 2. 2

Finding Values • Working backwards 1. Find given proportion in table Z (approximate) 2. Find corresponding z-score 3. “Un-standardize” to find the value

Example: Finding Values Scores on the SAT verbal test in recent years follow approximately the N(505, 110) distribution. How high must a student score in order to place in the top 10% of all students taking the SAT? Step 1: Look up proportion in Table A. Need to find SAT score x with area 0. 1 to its right under the normal curve with mean µ = 505 and standard deviation σ = 110. This is the same as find the score x with area 0. 9 to its left.

Example: Finding Values Scores on the SAT verbal test in recent years follow approximately the N(505, 110) distribution. How high must a student score in order to place in the top 10% of all students taking the SAT? Step 2: Find corresponding z-score

Example: Finding Values Scores on the SAT verbal test in recent years follow approximately the N(505, 110) distribution. How high must a student score in order to place in the top 10% of all students taking the SAT? Step 3: Sketch and “Un-standardize” to find value. z = 1. 28 is the standardized value for the top 10%. A student must score at least 645. 8 to be in the highest 10%

p. 130 (52, 53 -54 c, 60)