Normal Distribution Starters

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.

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.

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

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

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

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

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.

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.

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.

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.

The Normal Distribution Name:________________________.

Lesson 7 Confidence Intervals: The basics. Recall is the mean of the sample and s is the standard deviation of the sample. Where μ is the mean of the.

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.

Tueday 9/27 Day 1 2- Fill out your Agenda. Science Starter-

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

Created by Mr. Lafferty Maths Dept.

6.4: Applications of the Standard Normal Distribution

CHAPTER 6 Random Variables

Probability, Finding the Inverse Normal

Review Class test scores have the following statistics:

Chapter 6: Normal Distribution Review

Normal Distribution Links Standard Deviation The Normal Distribution

An Example of {AND, OR, Given that} Using a Normal Distribution

The Distribution Normality

WARM UP 1. A national investigation reveals that 24% of year olds get traffic tickets. You collect a random sample of year olds.

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

Bellwork Suppose that the average blood pressures of patients in a hospital follow a normal distribution with a mean of 108 and a standard deviation of.

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

Warm Up The weights of babies born in the “normal” range of weeks have been found to follow a roughly normal distribution. Mean Std. Dev Weight.

EXAMPLE: The weight of a can of Coca Cola is supposed to have mean = 12 oz with std. dev.= 0.82 oz. The product is declared underweight if it weighs.

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

Consider the following problem

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

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

Central Limit Theorem Accelerated Math 3.

Normal Distribution.

The Normal Distribution

Normal Distribution Starters

An Example of {AND, OR, Given that} Using a Normal Distribution

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 A Starter A Solns (z values) Starter B Starter B Solns A Starter B Solns B Starter C Starter C: Solns 1 Starter C: Solns 2 Starter D Starter D: Solns 1 Starter D: Solns 2 Starter E Starter E: Solns 1 Starter E: Solns 2 Starter F Starter F: Solns 1 Starter F: Solns 2 Starter G Starter G: Solns 1 Starter G: Solns 2 Starter H Starter H Solns (inverse z values) Starter I Starter I: Solns 1 Starter I: Solns 2

1st Page ‘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(-0.844 < 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 < -2.111) =

‘Z’ value Solutions 1st Page 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(-0.844 < 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 < -2.111) =

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

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

1st Page Starter B Solns 2 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) = 240mm 5) P(A fish is between 255 and 265mm long) = 240mm

1st Page Starter C A west coast population of mosquitoes have a Mean weight of 4.8kg Calculate the probability of the following (Std dev = 0.6kg) 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? 4.8kg 5) What percentage of mosquitoes are under 5.5kg?

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

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

Starter D 1st Page A room contains flies with a Mean weight of 3.6g and a Standard Deviation of 0.64kg 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? 3.6g 5) What percentage of flies are under 2.5g

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

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

1st Page Starter E The mean weight of a loader scoop of coal is 1.25 tonnes and a standard deviation of 280 kg 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? 1.25t 5) What percentage of scoops are between 1 tonne and 2 tonnes

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

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

1st Page Starter F The weight of glue paste Ralph eats in a day is normally distributed with a mean of 4.6kg & standard deviation of 1.3kg 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? 4.6kg 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? 5) What is the probability he does not eat between 3.5 & 5 kg of glue paste?

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

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

1st Page Starter G Itchy & Scratchy have a hammer collection which is normally distributed with a mean of 10.4 kg & standard deviation of 2.3kg 1) What percentage of the hammers weigh less than 8kg? 10.4kg 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? 5) 90% of hammers weigh more than what weight?

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

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

Inverse ‘Z’ values 1st Page 0 z Look up these probabilities to find the corresponding ‘z’ values 1) 2) 0.4 0.3 3) 4) 0.85 0.45 5) 6) 0.65 0.08 7) 8) 0.12 0.02

Inverse ‘Z’ values: Solns 1st Page Inverse ‘Z’ values: Solns 0 z Look up these probabilities to find the corresponding ‘z’ values 1) 2) 0.4 0.3 3) 4) 0.85 0.45 5) 6) 0.65 0.08 7) 8) 0.12 0.02

1st Page Starter I 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 1) What is the probability his blood loss is than 100mL? 120mL 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? 5) The middle 80% of blood losses are between what two amounts?

Starter I: Solns 1 1st Page 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 1) What is the probability his blood loss is than 100mL? 120mL 2) 80% of the time his blood loss is more then ‘M’ mL. Find the value of ‘M’ 120mL 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? 120mL

Starter I: Solns 2 1st Page 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 4) 30% of the time Kenny is not concerned by his blood loss? What is his blood loss when he starts to be concerned? 120mL 5) The middle 80% of blood losses are between what two amounts? 120mL Lucky Kenny is not involved in the knife catching competition!