7.3 Applications of the Normal Distribution Objectives- 1. Find and Interpret the area under a normal curve. 2. Find the value of a normal random variable Finding the Area under Any Normal Curve Step 1: Draw a normal curve and shade the designated area. Step 2: Convert the values of X to z-scores using Z=(X- ?)/ ?. Step 3: Draw a standard normal curve and shade the desired area. Step 4: Find the area under the standard normal curve. This area is equal to the area under the normal curve drawn in Step 1. Procedure for Finding the Value of a Normal Random Variable Corresponding to a Specified Proportion, Probability, or Percentile Step 1: Draw a normal curve and shade the area corresponding to the proportion, probability, or percentile. Step 2: Use Table V (from the appendix in the book) to find the z-score that corresponds to the shaded area. Step 3: Obtain the normal value from the formula x= ?+z ?.
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