Objective To find probability using standard normal distribution

Objective: To find probability using standard normal distribution. Standard 5. 10

Real life examples • 1. the distribution of heights of people in USA is normal distribution. • 2. the distribution of light bills of residents of South Carolina is normal distribution.

CHARACTERISTICS 1. bell-shaped 2. symmetric about mean 3. mean, median, mode equal 4. Continuous distribution 5. Never touch the x-axis 6. Area under curve is 1 7. unimodal

Many variables are normally distributed, and the distribution can be used to describe these variables.

What is the total area under the normal distribution curve? § 1 or 100%

What percentage of area falls below the mean? Above the mean? • 50%; 50%

Example 1: l Find P(0 < z < 2. 073) l Solution: Step 1: Draw normal distribution curve. Step 2: Plot z-values. Step 3: Shade the portion of the curve. Step 4: Use graphing utility to find the probability. l l l

Example 2: • Find P ( z > -1. 64) • Solution: Find the area to the right of z = -1. 64

Example 3: § Find P( z < 2. 049) § Solution: Find the area to the left of z = 2. 049

Find the area under the normal distribution curve between z=1. 345 and z= 2. 098 Solution: Use graphing calculator. Step 1: 2 nd DSTR Step 2: Select 2: normalcdf( Step 3: Type lower value of z first and higher value of z next. Step 4: Enter and get the area.

Z= 145/236, z= -0. 92538

1. z= -1. 26, z= -2. 098, z= -23/25 z= 223/145, z= 1. 7802, z= -0. 6720, z= 2. 654, z= 0. 2971, z= 1. 3864, z= 226/567, z= 2. 05 z= 2. 7649 z= 1. 0876 z= 2. 0987 z= 14/5 z= 1. 8937 z= -1. 6291 z= 0. 0728 z= 1. 9076 z= 123/189

Examples continue…. ØFind the area of the curve to the left of z=1. 967 ØFind the area of the curve to the right of z=0. 5206

Textbook: pages 311 -312: thru 39. problems 1