Chapter 7 The Normal Distribution and Its Applications

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: •

• Example 2) – 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 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. • and 2 are the parameters of the distribution. • If X is distributed in this way we write X N( , 2).

• 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?