CHAPTER7 Continuous Probability distributions to accompany Introduction to business statistics fourth edition by ronald m. weiers Presentation by priscilla chaffe-Stengel Donald N. Stengel o 2002 The Wadsworth Group
CHAPTER 7 Continuous Probability Distributions to accompany Introduction to Business Statistics fourth edition, by Ronald M. Weiers Presentation by Priscilla Chaffe-Stengel Donald N. Stengel © 2002 The Wadsworth Group
l Chapter 7-learning objectives Differentiate between the normal and the exponential distributions Use the standard normal distribution and z-scores to determine probabilities associated with the normal distribution Use the normal distribution to approximate the binomial distribution Use the exponential distribution to determine related probabilities o 2002 The Wadsworth Group
Chapter 7 - Learning Objectives • Differentiate between the normal and the exponential distributions. • Use the standard normal distribution and z-scores to determine probabilities associated with the normal distribution. • Use the normal distribution to approximate the binomial distribution. • Use the exponential distribution to determine related probabilities. © 2002 The Wadsworth Group
l Chapter 7-Key terms Probability density function Probability distributions Standard normal distribution >Mean, variance, applications Exponential distribution >> Mean, variance, applications Normal approximation to the binomial distribution o 2002 The Wadsworth Group
Chapter 7 - Key Terms •Probability density function •Probability distributions – Standard normal distribution »Mean, variance, applications – Exponential distribution »Mean, variance, applications • Normal approximation to the binomial distribution © 2002 The Wadsworth Group
l Chapter 7-Key concept The area under a probability density function between two bounds, a and b, is the probability that a value will occur within the bounded interval between a and b o 2002 The Wadsworth Group
Chapter 7 - Key Concept •The area under a probability density function between two bounds, a and b, is the probability that a value will occur within the bounded interval between a and b. © 2002 The Wadsworth Group
l The Normal distribution An important family of continuous distributions Bell-shaped, symmetric, and asymptotic To specify a particular distribution in this family, two parameters must be given Mean Standard deviation C 2002 The Wadsworth Group
The Normal Distribution • An important family of continuous distributions • Bell-shaped, symmetric, and asymptotic • To specify a particular distribution in this family, two parameters must be given: – Mean – Standard deviation © 2002 The Wadsworth Group
I Areas under the normal curve Use the standard normal table to find The z-score such that the area from the midpoint to z is 0.20 In the interior of the standard normal table, look up a value close to 0. 20 The closest value is 0.1985, which 20% occurs at f of the area z=0.52. o 2002 The Wadsworth Group
Areas under the Normal Curve Use the standard normal table to find: • The z-score such that the area from the midpoint to z is 0.20. In the interior of the standard normal table, look up a value close to 0.20. The closest value is 0.1985, which occurs at z = 0.52. © 2002 The Wadsworth Group 20% of the area z
I Areas under the normal curve Use the standard normal table to find ° The probability associated with z:P(0≤z≤1.32) Locate the row whose header is 1. 3. Proceed along that row to the column whose header is. 02. There you find the value, 4066, which is the amount of area capture between the e mean and a z of 1.32 Answer:0.4066 1.32 o 2002 The Wadsworth Group
Areas under the Normal Curve Use the standard normal table to find: • The probability associated with z: P(0 z 1.32). Locate the row whose header is 1.3. Proceed along that row to the column whose header is .02. There you find the value .4066, which is the amount of area capture between the mean and a z of 1.32. Answer: 0.4066 © 2002 The Wadsworth Group z = 1.32
I Areas under the normal curve Use the standard normal table to find: ° The probability associated with z:P(-110≤2≤1.32) Find the amount of area between the mean and z=1.32 and add it to the amount of area between the mean and z=1.10* 0.3643+04066=07709/aca2 z=?.10z=1.32 o 2002 The Wadsworth Group
Areas under the Normal Curve Use the standard normal table to find: • The probability associated with z: P(–1.10 z 1.32). Find the amount of area between the mean and z = 1.32 and add it to the amount of area between the mean and z = 1.10*. 0.3643 + 0.4066 = 0.7709 © 2002 The Wadsworth Group z = ? .10 z = 1.32 Area 1 Area 2
I Areas under the normal curve Dealing with negative z's Note- because the normal curve is symmetric, the amount of area between the mean and z=-1.10 is the same as the amount of area between the mean and z=+1.10 C 2002 The Wadsworth Group
Areas under the Normal Curve - Dealing with Negative Z’s • Note - Because the normal curve is symmetric, the amount of area between the mean and z = –1.10 is the same as the amount of area between the mean and z = +1.10. © 2002 The Wadsworth Group
I Areas under the normal Curve Use the standard normal table to find The probability associated with z: P(1.00<z< 1.32) Find the amount of area between the mean and z=1.00 and subtract it from the amount of area between the mean and z=1,32 0.4066-0.3413=0.0653 z=1.00 =1.32 C 2002 The Wadsworth Group
Areas under the Normal Curve Use the standard normal table to find: • The probability associated with z: P(1.00 z 1.32). Find the amount of area between the mean and z = 1.00 and subtract it from the amount of area between the mean and z = 1.32. 0.4066 – 0.3413 = 0.0653 © 2002 The Wadsworth Group z = 1.32 z = 1.00
