Chapter 7 The Normal Distribution and Its Applications

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Presentation transcript:

Chapter 7 The Normal Distribution and Its Applications 7.1 Standard normal distribution N(0,1) 7.2 Transform to 7.3 The Normal Distribution

7.1 Standard normal distribution N(0,1) , for Example Refer to p.414 Standard normal curve Given the standard normal variable Z ~ N(0,1), find the following probabilities:

Example2) Given the standard normal variable Z ~ N(0,1), find the following probabilities:

Example Refer to p.414 Standard normal curve Given the standard normal variable Z ~ N(0,1), find the following probabilities:

7.2 Transform to

7.3 The Normal Distribution The normal distribution is the most important continuous distribution in statistics. Many measured quantities in the natural sciences follow a normal distribution, for example heights, masses, ages, random errors, I.Q. scores, examination results. 7.3.1 The Probability Density Function  and 2 are the parameters of the distribution. If X is distributed in this way we write A continuous random variable X having p.d.f f(x) where -  < x <  is said to have a normal distribution with mean  and variance 2. X  N(, 2).

Application of Normal Distribution C.W. Application of Normal Distribution 1)If the time a student stays in a classroom follows the normal distribution with and , what is the probability that he stays in a classroom for less than 5 hours?