Objective: To find probability using standard normal distribution.

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Presentation transcript:

Objective: To find probability using standard normal distribution.

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: Find P(0 < z < 2.073) Solution: Step1: Draw normal distribution curve. Step2: Plot z-values. Step 3: Shade the portion of the curve. Step 4: Use graphing utility to find the probability.

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=  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=

 1. z= -1.26, z= 2.05  z= , z=  z= -23/25 z=  z= 223/145, z=  z= , z= 14/5  z= , z=  z= 2.654, z=  z= , z=  z= , z=  z= 226/567, z= 123/189

Examples continue….  Find the area of the curve to the left of z=1.967  Find the area of the curve to the right of z=0.5206

 Textbook: pages : problems 1 thru 39.