Download Lesson 7.3 Standard Units and Area Under the Standard Normal

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