Applications…….

Slides:

Advertisements

Similar presentations

Normal Distributions: Finding Probabilities 1 Section 5.2.

Advertisements

Section 5.2 Normal Distributions: Finding Probabilities 1 Larson/Farber 4th ed.

Normal Distributions: Finding Probabilities

Normal Distribution Calculations

5.3 The Central Limit Theorem. Roll a die 5 times and record the value of each roll. Find the mean of the values of the 5 rolls. Repeat this 250 times.

QBM117 Business Statistics Probability and Probability Distributions The Normal Distribution 1.

The Normal Distribution

The Normal Distribution

The normal distribution

Chapter 6 The Normal Distribution Section 6-3 The Standard Normal Distribution.

Warm-Up The probability that a person owns and I-phone is  What is the probability that in a random group of 10 people, at least 7 own an I-phone?

Statistics Sampling Distributions

Math 3Warm Up4/23/12 Find the probability mean and standard deviation for the following data. 2, 4, 5, 6, 5, 5, 5, 2, 2, 4, 4, 3, 3, 1, 2, 2, 3, 4, 6,

The Normal Distribution. Bell-shaped Density The normal random variable has the famous bell-shaped distribution. The most commonly used continuous distribution.

Sec 6.2 Bluman, Chapter Applications of the Normal Distributions The standard normal distribution curve can be used to solve a wide variety.

MATH104- Ch. 12 Statistics- part 1C Normal Distribution.

The Standard Normal Distribution

Chapter 6.3 The central limit theorem. Sampling distribution of sample means A sampling distribution of sample means is a distribution using the means.

6.3 THE CENTRAL LIMIT THEOREM. DISTRIBUTION OF SAMPLE MEANS  A sampling distribution of sample means is a distribution using the means computed from.

§ 5.3 Normal Distributions: Finding Values. Probability and Normal Distributions If a random variable, x, is normally distributed, you can find the probability.

An opinion poll asks, “Are you afraid to go outside at night within a mile of your home because of crime?” Suppose that the proportion of all adults who.

Chapter 6 The Normal Distribution Section 6-3 The Standard Normal Distribution.

Math 3 Warm Up 4/23/12 Find the probability mean and standard deviation for the following data. 2, 4, 5, 6, 5, 5, 5, 2, 2, 4, 4, 3, 3, 1, 2, 2, 3,

Continuous Probability Distribution By: Dr. Wan Azlinda Binti Wan Mohamed.

Unit 6 Section 6-4 – Day 1.

Chapter 6.2 Applications of the Normal Distribution.

STA 2023 Section 5.4 Sampling Distributions and the Central Limit Theorem.

Sec 6.3 Bluman, Chapter Review: Find the z values; the graph is symmetrical. Bluman, Chapter 63.

Chapter 7.2. The __________ of a discrete random variable, X, is its _________ _____________. Each value of X is weighted by its probability. To find.

Section 7.3 Sample Means. A look back at proportions… You may have noticed that proportions ALWAYS deal with categorical data. You may have noticed that.

Note: This PowerPoint is only a summary and your main source should be the book. Lecturer : FATEN AL-HUSSAIN The Normal Distribution.

Empirical Rule 68% 95% 99.7% % RULE Empirical Rule—restated 68% of the data values fall within 1 standard deviation of the mean in either direction.

THE CENTRAL LIMIT THEOREM. Sampling Distribution of Sample Means Definition: A distribution obtained by using the means computed from random samples of.

6.4 A PPLICATIONS OF THE N ORMAL D ISTRIBUTIONS. The standard normal distribution curve can be used to solve a wide variety of practical problems. The.

The Normal Distribution. Introduction  6-1 Properties of the Normal Distribution and the Standard Normal Distribution.  6-2 Applications of the Normal.

Sampling Distributions

CHAPTER 6 Random Variables

Chapter 6 Continuous Probability Distribution

Objectives Find probabilities for normally distributed variables

Finding Probability Using the Normal Curve

Confidence Interval of the Mean – Population St. Dev Unknown

Chapter 9.3: Sample Means Mr. Lynch AP Statistics.

Top, Middle, & Bottom Cutoff Scores……

6-3The Central Limit Theorem.

The Normal Distribution

The Normal Distribution

Chapter 5 Normal Probability Distributions

Random Variables Review Game

Handout THQ #5 at end of class.

Normal Distribution Many things closely follow a Normal Distribution:

The Normal Probability Distribution Summary

Chapter 5 Normal Probability Distributions.

Chapter 5 Normal Probability Distributions

Lesson #9: Applications of a Normal Distribution

Click the mouse button or press the Space Bar to display the answers.

Bell Work! How do you…?.

Normal Distribution.

Click the mouse button or press the Space Bar to display the answers.

Use the graph of the given normal distribution to identify μ and σ.

Suppose that the random variable X has a distribution with a density curve that looks like the following: The sampling distribution of the mean of.

Central Limit Theorem Accelerated Math 3.

AGENDA: DG minutes Begin Part 2 Unit 1 Lesson 11.

The normal distribution

Central Limit Theorem cHapter 18 part 2.

Combining Random Variables

Day 13 AGENDA: DG minutes Begin Part 2 Unit 1 Lesson 11.

Math 3 Warm Up 4/23/12 Find the probability mean and standard deviation for the following data. 2, 4, 5, 6, 5, 5, 5, 2, 2, 4, 4, 3, 3, 1, 2, 2, 3,

The Normal Distribution

Ch. 8 Central Limit Theorem 8.1: Sample means 8.2: Sample proportions

Chapter 5 Normal Probability Distributions.

Presentation transcript:

Applications……

OBJECTIVE Find probabilities using a normal distribution.

RELEVANCE Find probabilities and values of populations whose data can be represented with a normal distribution.

Application Problems…… Not all distributions are standard normal. You must use the z-score formula to transform normal to standard normal.

Example…… The mean # of hours an American worker spends on the computer is 3.1 hours per workday. Assume the st. deviation is 0.5 hours. Find the percentage of workers who spend less than 3.5 hours on the computer each workday.

Remember “less than 3.5”…. Mean = 3.1 Value = 3.5 St. Dev = 0.5 Answer: ncdf(-1000,0.8)= 0.7881 or 78.81%

You Try The incomes of trainees at a local mill are normally distributed with a mean of $1100 and a standard deviation of $150. What percentage of trainees earn less than $900 a month?

The incomes of trainees at a local mill are normally distributed with a mean of $1100 and a standard deviation of $150. What percentage of trainees earn less than $900 a month?

Example…… Each month, an American household generates an average of 28 pounds of newspapers for garbage or recycling. Assume the st. dev. is 2 lbs. If a household is selected at random, find the probability of its generating a. Between 27 and 31 pounds per mo. b. More than 30.2 pounds per month.

“Between 27 and 31 pounds”…… Value = 27 and 31 Mean = 28 St. Dev = 2 Answer: ncdf(-0.5,1.5) = 0.6247

“More Than 30.2……” Value = 30.2 Mean = 28 St. Dev = 2 Answer: ncdf(1.1,1000)= 0.1357

You Try The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches?

The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches?

You Try A bank’s loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 200 and 275.

A bank’s loan officer rates applicants for credit A bank’s loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 200 and 275.

Example…… The average time it takes to respond to an emergency call is 25 minutes. The variable is normally distributed and the st. dev is 4.5 minutes. If 80 calls are randomly selected, how many will respond in less than 15 minutes?

Value = 15 Mean = 25 St. Dev = 4.5 Answer: Find the percentage 1st. ncdf(-1000,-2.22) = 0.0132 This means that 1.32% of the 80 will respond in less than 15 minutes. (80)(.0132) = 1.056 = 1 call

Assignment…… HW Worksheet