EXAMPLE 3 Use a z-score and the standard normal table Scientists conducted aerial surveys of a seal sanctuary and recorded the number x of seals they observed.

Slides:

Advertisements

Similar presentations

Warm Up 1.What is the distance between the points (2, -5) and (-4, 7)? 2. Determine the center and radius for the circle with (-5, 2) and (3, -2) as endpoints.

Advertisements

60, 70, 78, 88, 88, 88, 93, 96 ________ Med = ___________ Mode = _________ Range = _________ __________ Warm-up.

Normal Distribution 2 To be able to transform a normal distribution into Z and use tables To be able to use normal tables to find and To use the normal.

How do I use normal distributions in finding probabilities?

Normal Distributions: Finding Values

Continuous Probability Distributions In this chapter, we’ll be looking at continuous probability distributions. A density curve (or probability distribution.

Normal Distributions Review

Chapter 11: Random Sampling and Sampling Distributions

6.3 Use Normal Distributions

§ 5.2 Normal Distributions: Finding Probabilities.

In 2009, the mean mathematics score was 21 with a standard deviation of 5.3 for the ACT mathematics section. ReferenceReference Draw the normal curve in.

Chapter Six Normal Curves and Sampling Probability Distributions.

Chapter 6: The Normal Probability Distribution This chapter is to introduce you to the concepts of normal distributions.  E.g. if a large number of students.

Using the Standard Normal Distribution to Solve SPC Problems

7.3 APPLICATIONS OF THE NORMAL DISTRIBUTION. PROBABILITIES We want to calculate probabilities and values for general normal probability distributions.

Normal Distribution Section 2.2. Objectives  Introduce the Normal Distribution  Properties of the Standard Normal Distribution  Use Normal Distribution.

Normal Distributions.

Continuous distributions For any x, P(X=x)=0. (For a continuous distribution, the area under a point is 0.) Can ’ t use P(X=x) to describe the probability.

Aim: what is the normal distribution? Do Now: Two sets of data given Find the mean.

Chapter 6.1 Normal Distributions. Distributions Normal Distribution A normal distribution is a continuous, bell-shaped distribution of a variable. Normal.

Normal Distributions.  Symmetric Distribution ◦ Any normal distribution is symmetric Negatively Skewed (Left-skewed) distribution When a majority of.

Normal Probability Distribution Using Normal Distribution for Probability.

Section 5.1 Discrete Probability. Probability Distributions x P(x)1/4 01/83/8 x12345 P(x)

Module 13: Normal Distributions This module focuses on the normal distribution and how to use it. Reviewed 05 May 05/ MODULE 13.

Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 1.

Table A & Its Applications - The entry in Table A - Table A’s entry is an area underneath the curve, to the left of z Table A’s entry is a proportion of.

Normal Probability Distributions. Intro to Normal Distributions & the STANDARD Normal Distribution.

The Standard Normal Distribution Section 5.2. The Standard Score The standard score, or z-score, represents the number of standard deviations a random.

7.4 Normal Distributions Part II p GUIDED PRACTICE From Yesterday’s notes A normal distribution has mean and standard deviation σ. Find the indicated.

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

INTRODUCTORY MATHEMATICAL ANALYSIS For Business, Economics, and the Life and Social Sciences  2011 Pearson Education, Inc. Chapter 16 Continuous Random.

Review Continuous Random Variables Density Curves

2.2 Standard Normal Calculations

EXAMPLE 1 Find a normal probability SOLUTION The probability that a randomly selected x -value lies between – 2σ and is the shaded area under the normal.

Chapter 6 The Normal Distribution.  The Normal Distribution  The Standard Normal Distribution  Applications of Normal Distributions  Sampling Distributions.

What does a population that is normally distributed look like? X 80  = 80 and  =

7.4 Use Normal Distributions p Normal Distribution A bell-shaped curve is called a normal curve. It is symmetric about the mean. The percentage.

STT Normal Distribution (Background) 6.3 Areas Under the Normal Curve 6.4 Application of the Normal Distribution.

© 2010 Pearson Prentice Hall. All rights reserved Chapter The Normal Probability Distribution © 2010 Pearson Prentice Hall. All rights reserved 3 7.

Chapter 9 – The Normal Distribution Math 22 Introductory Statistics.

7.4 Use Normal Distributions p Warm-Up From Page 261 (Homework.) You must show all of your work for credit 1.) #9 2.) #11.

Lecture 9 Dustin Lueker. 2  Perfectly symmetric and bell-shaped  Characterized by two parameters ◦ Mean = μ ◦ Standard Deviation = σ  Standard Normal.

Section 5.1 Discrete Probability. Probability Distributions x P(x)1/4 01/83/8 x12345 P(x)

Table A & Its Applications - The entry in Table A - Table A is based on standard Normal distribution N(0, 1) An area underneath the curve, less than z.

Copyright © 2015, 2012, and 2009 Pearson Education, Inc. 1 Chapter Normal Probability Distributions 5.

Normal Probability Distributions. Intro to Normal Distributions & the STANDARD Normal Distribution.

Unit 6 Section : Normal Distributions: Finding Probabilities  A normal distribution curve can be used as a probability distribution.  Remember,

Warm Up A normal distribution has a mean of and a standard deviation of 9.3. use the standard normal table on page 248 to find the indicated probability.

 A standardized value  A number of standard deviations a given value, x, is above or below the mean  z = (score (x) – mean)/s (standard deviation)

Normal Probability Distributions Chapter 5. § 5.2 Normal Distributions: Finding Probabilities.

7.4 Normal Distributions. EXAMPLE 1 Find a normal probability SOLUTION The probability that a randomly selected x -value lies between – 2σ and is.

Section 5.2 Normal Distributions: Finding Probabilities © 2012 Pearson Education, Inc. All rights reserved. 1 of 104.

Copyright © Cengage Learning. All rights reserved. 8 PROBABILITY DISTRIBUTIONS AND STATISTICS.

Objectives Find probabilities for normally distributed variables

Finding Probability Using the Normal Curve

Finding Probabilities

Probability, Finding the Inverse Normal

Use Normal Distributions

NORMAL PROBABILITY DISTRIBUTIONS

Sections 5-1 and 5-2 Quiz Review Warm-Up

Aim: what is the normal distribution?

Using the Normal Distribution

11-3 Use Normal Distributions

Using a standard normal table

How do I use normal distributions in finding probabilities?

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

STA 291 Summer 2008 Lecture 9 Dustin Lueker.

6.2 Use Normal Distributions

6.2 Use Normal Distributions

STA 291 Spring 2008 Lecture 9 Dustin Lueker.

Presentation transcript:

EXAMPLE 3 Use a z-score and the standard normal table Scientists conducted aerial surveys of a seal sanctuary and recorded the number x of seals they observed during each survey. The numbers of seals observed were normally distributed with a mean of 73 seals and a standard deviation of 14.1 seals. Find the probability that at most 50 seals were observed during a survey. Biology

EXAMPLE 3 Use a z-score and the standard normal table SOLUTION STEP 1 Find: the z -score corresponding to an x -value of 50. –1.6 z = x – x 50 – = STEP 2 Use: the table to find P(x < 50) P(z < – 1.6). The table shows that P(z < – 1.6) = So, the probability that at most 50 seals were observed during a survey is about

EXAMPLE 3 Use a z-score and the standard normal table

GUIDED PRACTICE for Example 3 8. WHAT IF? In Example 3, find the probability that at most 90 seals were observed during a survey ANSWER

GUIDED PRACTICE for Example 3 9. REASONING: Explain why it makes sense that P(z < 0) = 0.5. A z- score of 0 indicates that the z- score and the mean are the same. Therefore, the area under the normal curve is divided into two equal parts with the mean and the z- score being equal to 0.5. ANSWER