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Lesson 7.3 Standard Units and Area Under the Standard Normal Distribution Part 2 Notes Statistics Page 1 of 4 Standard Normal Distribution Normal distribution with mean µ = 0 and standard deviation σ = 1 Areas Under the standard Normal Curve To find the area under the standard normal curve, we use a left-tail style table. The table gives the cumulative area to the left of the z value. Example 1: Use the table given to find a. The area under the standard normal curve to the left of the z = -1.23. b. The area under the standard normal curve to the left of z = 2.1. c. The area under the standard normal curve to the left of z = -1.00. d. The area under the standard normal curve to the left of z = 1.18. Lesson 7.3 Standard Units and Area Under the Standard Normal Distribution Part 2 Notes Statistics Page 2 of 4 Example 2: Answer the following questions based on the Standard Normal Distribution table. a. As the z values increase, do the areas to the left of z increase? b. If a z value is negative, is the area to the left of z less than 0.5000? c. If a z value is positive, is the area to the left of z greater than 0.5000? d. If z < 0, is the area to the left of z less than or greater than 0.5? e. If z > 0, is the area to the left of z less than or greater than 0.5? f. As z values decrease, do the areas to the left of z increase? How to use a Left-Tail Style Standard Normal Distribution Table. 1. For the areas to the left of a specified z value, use the table entry directly. 2. For the areas to the right of a specified z value, look up the table entry for z and subtract the area from 1. 3. For the areas between two z values, z1 and z2 (where z2 > z1), subtract the table area for z1 from the table area for z2. Lesson 7.3 Standard Units and Area Under the Standard Normal Distribution Part 2 Notes Statistics Page 3 of 4 Notes: Treat any area to the left of a z value smaller than -3.49 as 0.000. Treat any area to the left of a z value greater than 3.49 as 1.000. Example 3: Use the table to find the specified areas. a. Find the area between z=1.00 and z= 2.70. b. Find the area to the right of z= 0.94. c. Find the area between z=0.5 and z= 1.5. d. Find the area to the right of z= 0.3. Example 4: Let z be a random variable with a standard normal distribution. a. P(z ≥ 1.15) refers to the probability that z values lie to the right of 1.15. Draw a normal distribution curve and shade the corresponding area under the standard normal curve and find P(z ≥ 1.15). Lesson 7.3 Standard Units and Area Under the Standard Normal Distribution Part 2 Notes Statistics Page 4 of 4 b. Find P(-1.78 ≤ z ≤ 0.35). First sketch a normal distribution curve and shade the area under the standard normal curve corresponding to the area. c. Find the probability P(z ≥ 1.89). d. Find the probability P(-1 < z ≤ 0.5). Assignment: p. 259 # 1, 4, 8, 11, 15, 21, 27, 29, 35, 41, 47