Normal Distribution Starters Starter AStarter A Starter A Solns (z values)Starter A Solns Starter BStarter B Starter B Solns A Starter B Solns BStarter.

Slides:

Advertisements

Similar presentations

The Normal Distribution

Advertisements

DP Studies Y2 Chapter 10: Normal Distribution. Contents: A. The normal distribution B. Probabilities using a calculator C. Quantiles or k-values.

The Central Limit Theorem Section 6-5 Objectives: – Use the central limit theorem to solve problems involving sample means for large samples.

1 Introduction to Inference Confidence Intervals William P. Wattles, Ph.D. Psychology 302.

The Normal Distribution

Sampling distributions. Example Take random sample of students. Ask “how many courses did you study for this past weekend?” Calculate a statistic, say,

Sampling distributions. Example Take random sample of 1 hour periods in an ER. Ask “how many patients arrived in that one hour period ?” Calculate statistic,

2-5 : Normal Distribution

Lecture 13: Review One-Sample z-test and One-Sample t-test 2011, 11, 1.

Transforms What does the word transform mean?. Transforms What does the word transform mean? –Changing something into another thing.

PROBABILITY AND SAMPLES: THE DISTRIBUTION OF SAMPLE MEANS.

6-5 The Central Limit Theorem

Warm Up The most common question asked was ‘why does the variance have to be equal to the mean?’ so let’s prove it! First you will need to explain.

Normal Distribution Links Standard Deviation The Normal Distribution Finding a Probability Standard Normal Distribution Inverse Normal Distribution.

The Central Limit Theorem. 1. The random variable x has a distribution (which may or may not be normal) with mean and standard deviation. 2. Simple random.

W ARM U P An unbiased coin is tossed 6 times. Our goal when tossing a coin is to get heads. Calculate: 1. At least 3 heads 2. At most 2 heads.

CHAPTER 7: CONTINUOUS PROBABILITY DISTRIBUTIONS. CONTINUOUS PROBABILITY DISTRIBUTIONS (7.1)  If every number between 0 and 1 has the same chance to be.

Sumukh Deshpande n Lecturer College of Applied Medical Sciences Statistics = Skills for life. BIOSTATISTICS (BST 211) Lecture 7.

Normal Distribution lesson 7

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

Stat 13, Tue 5/8/ Collect HW Central limit theorem. 3. CLT for 0-1 events. 4. Examples. 5.  versus  /√n. 6. Assumptions. Read ch. 5 and 6.

Probability Definition: randomness, chance, likelihood, proportion, percentage, odds. Probability is the mathematical ideal. Not sure what will happen.

Interpreting Performance Data

How confident can we be in our decisions?. Unit Plan – Week 3-6 (16 lessons)  Distributions – Normal and Otherwise  The Central Limit Theorem  Confidence.

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

Biostatistics, statistical software III. Population, statistical sample. Probability, probability variables. Important distributions. Properties of the.

L3.2 Confidence Intervals Starters Starters A B C D E F G H I J K L M NABCDEFGHIJKLMN.

The properties of a normal distribution: It is a bell-shaped curve. It is symmetrical about the mean, μ. (The mean, the mode and the median all have the.

Sampling Distributions-Chapter The Central Limit Theorem 7.2 Central Limit Theorem with Population Means 7.3 Central Limit Theorem with Population.

Statistics 300: Elementary Statistics Section 6-5.

Distribution of the Sample Mean (Central Limit Theorem)

The Central Limit Theorem 1. The random variable x has a distribution (which may or may not be normal) with mean and standard deviation. 2. Simple random.

Starter The length of leaves on a tree are normally distributed with a mean of 14cm and a standard deviation of 4cm. Find the probability that a leaf is:

381 Continuous Probability Distributions (The Normal Distribution-II) QSCI 381 – Lecture 17 (Larson and Farber, Sect )

Meta-Study. Representation of the Sampling Distribution of Y̅

Normal Distribution Links The Normal Distribution Finding a Probability Standard Normal Distribution Inverse Normal Distribution.

40S Applied Math Mr. Knight – Killarney School Slide 1 Unit: Statistics Lesson: ST-4 Standard Scores and Z-Scores Standard Scores and Z-Scores Learning.

Section 7.2 Central Limit Theorem with Population Means HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant.

Solving Trig Equations Starter CStarter C Starter C SolutionsStarter C Solutions Starter DStarter D Starter D SolutionsStarter D Solutions.

Discrete and Continuous Random Variables. Yesterday we calculated the mean number of goals for a randomly selected team in a randomly selected game.

7-1 and 7-2 Sampling Distribution Central Limit Theorem.

Inverse Normal Calculations. Consider a population of crabs where the length of a shell, X mm, is normally distributed with a mean of 70mm and a standard.

Significance Tests Section Cookie Monster’s Starter Me like Cookies! Do you? You choose a card from my deck. If card is red, I give you coupon.

3.5 Applying the Normal Distribution – Z Scores Example 1 Determine the number of standard deviations above or below the mean each piece of data is. (This.

Distributions of Sample Means. z-scores for Samples  What do I mean by a “z-score” for a sample? This score would describe how a specific sample is.

Statistical Analysis – Chapter 5 “Central Limit Theorem” Dr. Roderick Graham Fashion Institute of Technology.

The Normal Distribution Name:________________________.

Binomial A 1) On average one bowl in every 4 has lumpy porridge. If big daddy B has 6 bowls of porridge, find the probability: (a) There are exactly 5.

Chem. 31 – 9/18 Lecture.

The Central Limit Theorem

STANDARD ERROR OF SAMPLE

Starter The weights of newborn lambs on a farm are normally distributed with a mean of 2.4kg and a standard deviation of 200g.

The Normal Distribution

Probability, Finding the Inverse Normal

Review Class test scores have the following statistics:

Normal Distribution Links Standard Deviation The Normal Distribution

Warm Up If there are 2000 students total in the school, what percentage of the students are in each region?

Warm Up If there are 2000 students total in the school, what percentage of the students are in each region?

Normal Distribution Starters

Test criterion and sampling distribution of x with m= 0.38 second.

If the question asks: “Find the probability if...”

Central Limit Theorem Accelerated Math 3.

Normal Distribution.

The Normal Distribution

Normal Distribution Starters

Warm Up Your textbook provides the following data on the height of men and women. Mean Std. Dev Men Women ) What is the z score.

Consider the following problem

Z-Scores and The Standard Normal Distribution

Presentation transcript:

Normal Distribution Starters Starter AStarter A Starter A Solns (z values)Starter A Solns Starter BStarter B Starter B Solns A Starter B Solns BStarter B Solns AStarter B Solns B Starter CStarter C Starter C: Solns 1 Starter C: Solns 2Starter C: Solns 1Starter C: Solns 2 Starter DStarter D Starter D: Solns 1 Starter D: Solns 2Starter D: Solns 1Starter D: Solns 2 Starter EStarter E Starter E: Solns 1 Starter E: Solns 2Starter E: Solns 1Starter E: Solns 2 Starter FStarter F Starter F: Solns 1 Starter F: Solns 2Starter F: Solns 1Starter F: Solns 2 Starter GStarter G Starter G: Solns 1 Starter G: Solns 2Starter G: Solns 1Starter G: Solns 2 Starter HStarter H Starter H Solns (inverse z values)Starter H Solns Starter IStarter I Starter I: Solns 1 Starter I: Solns 2Starter I: Solns 1Starter I: Solns 2

‘Z’ values 0 z Look up these ‘z’ values to find the corresponding probabilities 1) P(0 < z < 1.4) =2) P(0 < z < 2.04) = 3) P(0 < z < 1.55) =4) P(0 < z < 2.125) = 5) P( < z < 0) =6) P(-2.44 < z < 2.44) = 7) P(-0.85 < z < 1.646) =8) P( z < 2.048) = 9) P(1.955 < z < 2.044) =10) P( z < ) = 1 st Page

‘Z’ value Solutions 0 z Look up these ‘z’ values to find the corresponding probabilities 1) P(0 < z < 1.4) =2) P(0 < z < 2.04) = 3) P(0 < z < 1.55) =4) P(0 < z < 2.125) = 5) P( < z < 0) =6) P(-2.44 < z < 2.44) = 7) P(-0.85 < z < 1.646) =8) P( z < 2.048) = 9) P(1.955 < z < 2.044) =10) P( z < ) = 1 st Page

Starter B 240mm A salmon farm water tank contains fish with a Mean length of 240mm Calculate the probability of the following (Std dev = 15mm) 1) P(A fish is between 240 and 250mm long) = 2) P(A fish is between 210 and 260mm long) = 3) P(A fish is less than 254mm long) = 4) P(A fish is less than 220mm long) = 5) P(A fish is between 255 and 265mm long) = 1 st Page

Starter B Solns 1 240mm A salmon farm water tank contains fish with a Mean length of 240mm Calculate the probability of the following (Std dev = 15mm) 1) P(A fish is between 240 and 250mm long) = 2) P(A fish is between 210 and 260mm long) = 3) P(A fish is less than 254mm long) = 1 st Page

Starter B Solns 2 240mm A salmon farm water tank contains fish with a Mean length of 240mm Calculate the probability of the following (Std dev = 15mm) 4) P(A fish is less than 220mm long) = 5) P(A fish is between 255 and 265mm long) = 1 st Page

Starter C 4.8kg A west coast population of mosquitoes have a Mean weight of 4.8kg Calculate the probability of the following (Std dev = 0.6kg) 5) What percentage of mosquitoes are under 5.5kg? 1 st Page 1) What is the probability a mosquito is between 4.8kg and 5.8kg? 2) What percentage of mosquitoes are between 4kg and 5kg? 3) Out of a sample of 120 mosquitoes, how many would be over 6kg? 4) What percentage of mosquitoes are between 3kg and 4kg?

Starter C: Solns 1 4.8kg A west coast population of mosquitoes have a Mean weight of 4.8kg Calculate the probability of the following (Std dev = 0.6kg) 1 st Page 1) What is the probability a mosquito is between 4.8kg and 5.8kg? 2) What percentage of mosquitoes are between 4kg and 5kg? 4.8kg

Starter C: Solns 2 4.8kg A west coast population of mosquitoes have a Mean weight of 4.8kg Calculate the probability of the following (Std dev = 0.6kg) 5) What percentage of mosquitoes are under 5.5kg? 1 st Page 3) Out of a sample of 120 mosquitoes, how many would be over 6kg? 4) What percentage of mosquitoes are between 3kg and 4kg? 4.8kg

Starter D 1 st Page 3.6g 5) What percentage of flies are under 2.5g 1) What is the probability a fly is between 3.6g and 5.8g? 2) What percentage of flies are between 3g and 5g? 3) Out of a sample of 40 flies, how many would be under 4g? 4) What percentage of flies are between 2g and 3g? A room contains flies with a Mean weight of 3.6g and a Standard Deviation of 0.64kg

Starter D: Solns 1 1 st Page 3.6g 1) What is the probability a fly is between 3.6g and 5.8g? 2) What percentage of flies are between 3g and 5g? A room contains flies with a Mean weight of 3.6g and a Standard Deviation of 0.64kg 3.6g

Starter D: Solns 2 1 st Page 3.6g 5) What percentage of flies are under 2.5g 3) Out of a sample of 40 flies, how many would be under 4g? 4) What percentage of flies are between 2g and 3g? A room contains flies with a Mean weight of 3.6g and a Standard Deviation of 0.64kg 3.6g

Starter E 1 st Page 1.25t 5) What percentage of scoops are between 1 tonne and 2 tonnes 1) What percentage of scoops are between 1.3 and 1.5 tonnes? 2) What percentage of scoops are less than 1 tonne? 3) Out of a sample of 500 scoops, how many would be over 1.4 tonnes? 4) What percentage of scoops are more than 1.6 tonnes? The mean weight of a loader scoop of coal is 1.25 tonnes and a standard deviation of 280 kg

Starter E: Solns 1 1 st Page 1.25t 1) What percentage of scoops are between 1.3 and 1.5 tonnes? 2) What percentage of scoops are less than 1 tonne? The mean weight of a loader scoop of coal is 1.25 tonnes and a standard deviation of 280 kg 1.25t

Starter E: Solns 2 1 st Page 1.25t 5) What percentage of scoops are between 1 tonne and 2 tonnes 3) Out of a sample of 500 scoops, how many would be over 1.4 tonnes? 4) What percentage of scoops are more than 1.6 tonnes? The mean weight of a loader scoop of coal is 1.25 tonnes and a standard deviation of 280 kg 1.25t

Starter F 1 st Page 4.6kg 5) What is the probability he does not eat between 3.5 & 5 kg of glue paste? 1) How many days in November will Ralph eat less than 5.5kg of glue paste? 2) What percentage of days does he eat less than 4kg of glue paste? 3) Ralph vomits when he eats more than 6kg of glue in a day. What is the chance of this happening? 4) What percentage of days does he eat between 4.2kg and 5kg of glue? The weight of glue paste Ralph eats in a day is normally distributed with a mean of 4.6kg & standard deviation of 1.3kg

Starter F: Solns 1 1 st Page 4.6kg 1) How many days in November will Ralph eat less than 5.5kg of glue paste? 2) What percentage of days does he eat less than 4kg of glue paste? The weight of glue paste Ralph eats in a day is normally distributed with a mean of 4.6kg & standard deviation of 1.3kg 4.6kg

Starter F: Solns 2 1 st Page 4.6kg 5) What is the probability he does not eat between 3.5 & 5 kg of glue paste? 3) Ralph vomits when he eats more than 6kg of glue in a day. What is the chance of this happening? 4) What percentage of days does he eat between 4.2kg and 5kg of glue? The weight of glue paste Ralph eats in a day is normally distributed with a mean of 4.6kg & standard deviation of 1.3kg 4.6kg

Starter G 1 st Page 10.4kg 5) 90% of hammers weigh more than what weight? 1) What percentage of the hammers weigh less than 8kg? 2) What is the probability a hammer weighs between 11kg & 14kg? 3) Scratchy’s head splits open if the hammer is more than 15kg. What is the chance of this happening? 4) A truck is loaded with 200 hammers. How many of these would be 12kg or less? Itchy & Scratchy have a hammer collection which is normally distributed with a mean of 10.4 kg & standard deviation of 2.3kg

Starter G: Solns 1 1 st Page 10.4kg 1) What percentage of the hammers weigh less than 8kg? 2) What is the probability a hammer weighs between 11kg & 14kg? Itchy & Scratchy have a hammer collection which is normally distributed with a mean of 10.4 kg & standard deviation of 2.3kg) 10.4kg

Starter G: Solns 2 1 st Page 10.4kg 5) 90% of hammers weigh more than what weight? 3) Scratchy’s head splits open if the hammer is more than 15kg. What is the chance of this happening? 4) A truck is loaded with 200 hammers. How many of these would be 12kg or less? Itchy & Scratchy have a hammer collection which is normally distributed with a mean of 10.4 kg & standard deviation of 2.3kg) 10.4kg

Inverse ‘Z’ values 0 z Look up these probabilities to find the corresponding ‘z’ values 1) 2) 5) 6) 7) 8) 1 st Page 3) 4)

Inverse ‘Z’ values: Solns 0 z Look up these probabilities to find the corresponding ‘z’ values 1) 2) 5) 6) 7) 8) 1 st Page 3) 4)

Starter I 1 st Page 120mL 5) The middle 80% of blood losses are between what two amounts? 1) What is the probability his blood loss is than 100mL? 2) 80% of the time his blood loss is more then ‘M’ mL. Find the value of ‘M’ 3) Kenny passes out when his blood loss is too much. This happens 5% of the time. What is the maximum amount of blood loss Kenny can sustain? 4) 30% of the time Kenny is not concerned by his blood loss? What is his blood loss when he starts to be concerned? Kenny is practicing to be in a William Tell play. He suffers some blood loss which is normally distributed with a mean of 120mL & standard deviation of 14mL

Starter I: Solns 1 1 st Page 120mL 1) What is the probability his blood loss is than 100mL? 2) 80% of the time his blood loss is more then ‘M’ mL. Find the value of ‘M’ 3) Kenny passes out when his blood loss is too much. This happens 5% of the time. What is the maximum amount of blood loss Kenny can sustain? Kenny is practicing to be in a William Tell play. He suffers some blood loss which is normally distributed with a mean of 120mL & standard deviation of 14mL 120mL

Starter I: Solns 2 1 st Page 120mL 5) The middle 80% of blood losses are between what two amounts? 4) 30% of the time Kenny is not concerned by his blood loss? What is his blood loss when he starts to be concerned? Kenny is practicing to be in a William Tell play. He suffers some blood loss which is normally distributed with a mean of 120mL & standard deviation of 14mL Lucky Kenny is not involved in the knife catching competition! 120mL