1. 1 Business 90: Business Statistics Professor David Mease Sec 03, T R 7:30-8:45AM BBC 204 Lecture 18 = Start Chapter “The Normal Distribution and Other Continuous Distributions” (TNDAOCD) Agenda: 1) Go over Homework 6 2) Assign Homework 7 (due Thursday 4/22) 3) Start Chapter TNDAOCD 4) Take quiz over Homework 6

2. 2 Homework 6 – Due Tuesday 4/13 1) Read chapter entitled “Some Important Discrete Probability Distributions” but only sections 1-3. 2) In that chapter do textbook problems 3, 4, 14, 15 and 20 (but skip part g in 20) 3) Stock X has a mean of $50 and a standard deviation of $10. Stock Y has a mean of $100 and a standard deviation of $20. Find the mean and standard deviation of buying one share of each A) If they are independent (so the covariance is 0) B) If the covariance is 30 C) If the covariance is -30

3. 3 1) Read chapter entitled “The Normal Distribution and Other Continuous Distributions” but only sections 1, 5 and 6. 2) In that chapter do textbook problems 6, 8, 38 and 44. Homework 7 – Due Thursday 4/22

4. 4 The Normal Distribution and Other Continuous Distributions Statistics for Managers Using Microsoft ® Excel 4 th Edition

5. 5 Chapter Goals After completing this chapter, you should be able to: Describe the characteristics of the normal distribution Translate normal distribution problems into standardized normal distribution problems Find probabilities using a normal distribution table Define the concept of a sampling distribution Determine the mean and standard deviation for the sampling distribution of the sample mean Describe the Central Limit Theorem and its importance Apply the sampling distribution for the sample mean

6. 6 Probability Distributions Random Variable Represents a possible numerical value from an uncertain event Random Variables Discrete Random Variable Continuous Random Variable (Previous Chapter) (This Chapter)

7. 7 Continuous Probability Distributions A continuous random variable is a variable that can assume any value on a continuum (can assume an uncountable number of values) thickness of an item time required to complete a task temperature of a solution height, in inches These can potentially take on any value, depending only on the ability to measure accurately.

8. 8 The Normal Distribution

9. 9 ‘Bell Shaped’ Symmetrical Mean, Median and Mode are Equal Location is determined by the mean, μ Spread is determined by the standard deviation, σ The random variable has an infinite theoretical range: +  to   Mean = Median X f(X) μ σ

10. 10 By varying the parameters μ and σ, we obtain different normal distributions Many Normal Distributions

11. 11 The formula for the normal probability density function is Where e = the mathematical constant approximated by 2.71828 π = the mathematical constant approximated by 3.14159 μ = the population mean σ = the population standard deviation X = any value of the continuous variable The Normal Distribution

12. 12 The Normal Distribution You can obtain probabilities for the normal distribution using table 2 You can look up Z (the number of standard deviations above or below the mean) on the left and top of this table and then the numbers inside the table will give you the probabilities to the LEFT of Z Z

13. 13 In class exercise #75: Use table 2 to determine the probability that a normally distributed random variable is less than 1 standard deviation above the mean.

14. 14 In class exercise #76: Use table 2 to determine the probability that a normally distributed random variable is greater than 1.6 standard deviations above the mean.

15. 15 In class exercise #77: Use table 2 to determine the probability that a normally distributed random variable is greater than 1.63 standard deviations above the mean.

16. 16 In class exercise #78: Use table 2 to determine the probability that a normally distributed random variable is greater than 2.34 standard deviations below the mean.

17. 17 In class exercise #79: Use table 2 to determine the probability that a normally distributed random variable is less than two standard deviations above the mean but greater than two standard deviations below the mean. Where have you seen this probability before?