Download presentation

Presentation is loading. Please wait.

Published byAubrey Godwin Modified over 2 years ago

1
Probability Distributions and the Binomial Distribution BUSA 2100, Sections 5.1 - 5.4

2
Random Variables l A random variable is a quantity that changes values from one occurrence to another, in no particular pattern. l Example 1: Let X = number of heads on 3 tosses of a coin; X = 0, 1, 2, 3. l Example 2: Let Y = number of papers sold daily in a newspaper rack; Y = 0, 1, 2, 3, 4, 5.

3
Discrete and Continuous Random Variables l A discrete random variable can have only a small number of specific possible values (usually whole numbers). It tells “how many.” The random variables in Examples 1, 2 are discrete. l A continuous random variable can have an undetermined large finite number of values. It tells “how much.”

4
Continuous Random Variables l Example 3: Let W = amount of time in minutes that a family watches TV in a month. This is a continuous random variable. l Example 4: Weight and distance are also continuous random variables.

5
Probability Distributions l A probability distribution (for a discrete random variable) is a list of all possible outcomes together with their associated probabilities. l State probability distribution for 3 coins.

6
Expected Value l What is the “average” value for X for the probability XP(X) distribution 60.1 shown at70.2 the right? 80.3 90.4 l The median is 75; the simple average is 75; is there a more accurate answer?

7
Expected Value, Page 2 l.l.

8
Republican/Democrat Ex. l Ex. 1A: A large group of people consists of 40% Republicans and 60% Demo- crats. If a sample of 5 is chosen, what is the probability of getting 2 Republicans and 3 Democrats, in that order?

9
Rep/Dem Example, Page 2 l Ex. 1B: What is the prob. of choosing 2 Repub. and 3 Democrats in any order?

10
Rep/Dem Example, Page 3 l To avoid listing the number of ways that 2 R’s and 3 D’s can be arranged, we can use combinations to determine how many ways we can choose which two of the 5 selections will be Republicans. l The Republican/Democrat problem is an example of the binomial distribution.

11
Intro. to Binomial Distribution l Binomial problems have 2 characteristics (requirements). l (1) Most important characteristic: Each selection must have exactly two possible outcomes. l Examples: l (2) Each selection is independent of the other selections.

12
Binomial Notation & Formula l Do each item for Rep./Dem. problem. l n = number of selections l Define “success”. l p = probability of success on one selection l r = number of successes

13
Binomial Problems, Page 1 l Example 1: A large lot of manufactured items contains 10% defectives. In a random sample of 6 items, what is the probability that exactly 2 are defective? l

14
Binomial Problems, Page 2 l Example 2: Thirty percent of customers that enter an appliance store make pur- chases. What is the prob. that 4 of the next 10 customers will buy something?

15
Binomial Problems, Page 3 l For convenience we will use a binomial table, looking up n, p, r, in that order. l Example 3A: A large lot of manufac- tured items contains 20% defectives. In a random sample of 8 items, what is the probability that 5 or more items are defective?

16
Binomial Problems, Page 4 l Ex. 3B: P(2 or fewer) =

17
Binomial Problems, Page 5 l Example 4: Sixty percent of the workers in a plant belong to a union. A random sample of 12 is chosen. Find the prob- ability that exactly 4 belong to a union.

18
Binomial Problems, Page 6 l.l.

19
Binomial Problems, Page 7 l Example 5: At Blaylock Company, in the past, 25% of new employees were not hired for a permanent position after a six-months probationary period. Among 7 new employees, what is the prob. that 5 or more will be hired permanently?

20
Binomial Problems, Page 8 l It is essential that the values of p and r are consistent with the way that success is defined.

Similar presentations

Presentation is loading. Please wait....

OK

Discrete Probability Distributions

Discrete Probability Distributions

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on levels of organization Ppt on taj hotel mumbai Ppt on eye os mean Ppt on mobile apps Ppt on waves tides and ocean currents powerpoint Ppt on solid state drives Ppt on induced abortion Ppt on c language fundamentals reviews Ppt on solar system formation Ppt on polluted ganga river