Normal Distribution Calculations

Slides:

Advertisements

Similar presentations

Normal Distribution Calculations. State: Express the problem in terms of the observed variable x. Plan: Draw a picture of the distribution and shade the.

Advertisements

Normal Distributions Ch. 6 Day 1 AP Statistics

Get out your Standard Normal WS! You will be able to use a four-step method to solve Normal distribution problems. Today’s Objectives:

Chapter 2: Modeling Distributions of Data

Practice Using the Z-Table

Warm-Up Grab a sheet of multiple choice questions and work on those!

The Normal Distribution

Homework for 2.1 Day 1: 41, 43, 45, 47, 49, 51. 1) To use the rule to estimate the percent of observations from a Normal Distribution that.

The Normal Distribution

Applying the Standard Normal Distribution to Problems

+ Chapter 2: Modeling Distributions of Data Section 2.2 Normal Distributions The Practice of Statistics, 4 th edition - For AP* STARNES, YATES, MOORE.

1 Copyright © 2015 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. C H A P T E R S I X The Normal Distribution.

Normal Distribution Z-scores put to use!

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?

Using the Empirical Rule. Normal Distributions These are special density curves. They have the same overall shape  Symmetric  Single-Peaked  Bell-Shaped.

Chapter 6 The Normal Distribution 1 Copyright © 2012 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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

+ Chapter 2: Modeling Distributions of Data Section 2.2 Normal Distributions The Practice of Statistics, 4 th edition - For AP* STARNES, YATES, MOORE.

+ Warm Up The graph below shows cumulative proportions plotted against GPA for a large public high school. What is the median GPA? a) 0.8b) 2.0c) 2.4d)

Section 2.2 Normal Distributions Mrs. Daniel AP Statistics.

Warm-Up On the driving range, Tiger Woods practices his golf swing with a particular club by hitting many, many balls. When Tiger hits his driver, the.

+ Chapter 2: Modeling Distributions of Data Section 2.2 Normal Distributions The Practice of Statistics, 4 th edition - For AP* STARNES, YATES, MOORE.

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

Chapter 7: The Normal Distribution. Important Properties of a Normal Distribution The mean, median, and mode have the same value, which is located exactly.

Chapter 2 Modeling Distributions of Data Objectives SWBAT: 1)Find and interpret the percentile of an individual value within a distribution of data. 2)Find.

+ Chapter 2: Modeling Distributions of Data Lesson 2: Normal Distributions.

SWBAT: Describe and Apply the Rule and the standard Normal Distribution. Do Now: Scott was one of 50 junior boys to take the PSAT at his school.

APPLICATIONS OF THE NORMAL DISTRIBUTION

Unit 6 Section 6-4 – Day 1.

+ Chapter 2: Modeling Distributions of Data Section 2.2 Normal Distributions The Practice of Statistics, 4 th edition - For AP* STARNES, YATES, MOORE.

Chapter 6.2 Applications of the Normal Distribution.

Upon reaching orbit the Space Shuttle will engage in MECO (Main Engine Cut-Off). At that time it will be traveling at an average of 17,580mph (σ = 35mph).

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

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.

Normal Distributions. Homework Answers 1. a) Her percentile is.25, or the 25 th percentile. 25% of girls have fewer pairs of shoes b) His.

2.2 Normal Distributions

Chapter 2: Modeling Distributions of Data

Chapter 2: Modeling Distributions of Data

Chapter 2: Modeling Distributions of Data

Entry Task Chapter 2: Describing Location in a Distribution

Top, Middle, & Bottom Cutoff Scores……

The Normal Distribution

Statistics Objectives: The students will be able to … 1. Identify and define a Normal Curve by its mean and standard deviation. 2. Use the 68 – 95 – 99.7.

Chapter 2: Modeling Distributions of Data

Chapter 2: Modeling Distributions of Data

What % of Seniors only apply to 3 or less colleges?

WARM – UP Jake receives an 88% on a Math test which had a N(81, 8). That same day he takes an English test N(81, 12) and receives a 90%. Which test did.

Warmup What is the height? What proportion of data is more than 5?

Chapter 2: Modeling Distributions of Data

Normal Distributions, Empirical Rule and Standard Normal Distribution

Chapter 2: Modeling Distributions of Data

Lesson #9: Applications of a Normal Distribution

Chapter 2: Modeling Distributions of Data

Chapter 2: Modeling Distributions of Data

More Normal Distribution Practice!

Chapter 3 Modeling Distributions of Data

Chapter 3: Modeling Distributions of Data

Chapter 2: Modeling Distributions of Data

Chapter 2: Modeling Distributions of Data

Chapter 2: Modeling Distributions of Data

Chapter 2: Modeling Distributions of Data

Chapter 2: Modeling Distributions of Data

Chapter 2: Modeling Distributions of Data

Mean and Median.

Chapter 2: Modeling Distributions of Data

Chapter 2: Modeling Distributions of Data

Presentation transcript:

Normal Distribution Calculations

Using the 4-step Process State: Express in terms of the observed variable x. Plan: Draw a picture of the distribution and shade the area of interest. Do: Perform calculations Standardize x Use the table Conclude: Write your conclusion in the context of the problem.

State: Plan: Do: Conclude: When Tiger Woods hits his driver, the distance the ball travels follows a Normal Distribution with mean 304 yards and standard deviation 8 yards. What percent of Tiger’s drives travel at least 290 yards? State: Plan: Do: Conclude: Let x = the distance Tiger’s ball travels and it has a distribution N(304, 8). We want P(x  290). About 96% of Tigers drives travel at least 290 yards.

Scores for a test have a mean of 100 and standard deviation of 15 Scores for a test have a mean of 100 and standard deviation of 15. Find the probability that a score is below 112.

Every month, American households generate an average of 28 pounds of newspaper for garbage or recycling. Assume =2 pounds. If a household is selected at random, find the probability that it generates between 27 and 31 pounds per month.

An exclusive college desires to accept only the top 10% of all graduating seniors based on the results of a national placement test. This test has a mean of 500 and a standard deviation of 100. Find the cutoff score for the exam.

For a medical study a researcher wishes to select people in the middle 60% of the population based on blood pressure. If the mean systolic blood pressure is 120 and the standard deviation is 8, find the upper and lower reading that would qualify a person to be in the study.

In the 2008 Wimbledon tennis tournament, Rafael Nadal averaged 115 miles per hour (mph) on his first serves. Assume that the distribution of his first serve speeds is Normal with a mean of 115 mph and a standard deviation of 6 mph. About what proportion of his first serves would you expect to exceed 120 mph?

What percent of Rafael Nadal’s first serves are between 100 and 110 mph? N(115, 6)

According to http://www. cdc According to http://www.cdc.gov/growthcharts/, the heights of 3 year old females are approximately Normally distributed with a mean of 94.5 cm and a standard deviation of 4 cm. What is the third quartile of this distribution?

Homework Worksheet (not the book problems listed)