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Algebra II/Unit4/MSDE Lesson Plan/Let’s Roll the Dice: Introduction of the Normal Distribution

 Supporting Information Details Interventions/Enrichments Special Education/Struggling Learners ELL Gifted and Talented Gifted and Talented: Students will be able to use normal probabilities to perform statistical significance tests and develop appropriate confidence intervals. Special Education/Struggling Learners: Teacher will have prepared data collection sheets with data/axes/histogram, normal calculations completed prior to lesson, based on student needs. Materials Student: Six-sided number cubes, “Let’s Roll the Dice” Worksheet, What is Normal Note Page, , graph paper, ruler , Normal Sketch Practice WS Teacher: What is Normal PowerPoint (or .pdf) Technology Calculators

Warm Up

Given the data set:

Test scores: 85, 84, 87, 92, 75, 86, 94, 99,100

1. Determine the mean and standard deviation and describe

its meaning in the context of the situation.

1. Construct a histogram and describe its center, shape and spread (variability).

Given the data set:

Test scores: 85, 84, 87, 92, 75, 86, 94, 99,100

1. Determine the mean and standard deviation and describe

its meaning in the context of the situation.

Mean

Standard Deviation

Add the squares of the deviations from the mean.

Divide the sum of the deviations from the mean by a number that is one less than the number of data values. (This is the formula used when the data set is a sample and not a population.)

Take the square root of the quotient from the previous step

The standard deviation is a measure of spread or variance. In this example the standard deviation tells us that that the distribution of test scores is somewhat clustered around the mean. In other words most of the student’s test scores fell within approximately 8 points of 89%.

1. Construct a histogram and describe its center, shape and spread (variability).
 3 2 1 70-75 76-80 81-85 86-90 91-95 96-100

Let’s Roll the Dice

Activity 1

1. Roll one 6-sided number cube 18 times. Record a tally mark next to the appropriate number after each roll. After rolling the cube 18 times, determine the frequency for each number by counting the tally marks.

 Individual Data Number Rolled Tally Marks Frequency 1 2 3 4 5 6

1. Create a histogram or bar graph for your individual data.

1. Determine the value of each of the following for your data set.

1. Mean

2. Median

3. Mode

4. Range

5. Interquartile Range

6. Standard Deviation

1. Record the combined class totals in the table below.

 Number Rolled Frequency 1 2 3 4 5 6

1. Create a histogram or bar graph for the class data.

1. Determine the value of each of the following of the Class data set.

1. Mean

2. Median

3. Mode

4. Range

5. Interquartile Range

6. Standard Deviation

Activity 2

 Individual Data Sum of the Numbers Rolled Tally Marks Frequency 2 3 4 5 6 7 8 9 10 11 12

Roll two 6-sided number cubes 18 times. Record a tally mark next to the appropriate number after each roll. After rolling the cube 18 times, determine the frequency for each number by counting the tally marks.

1. Create a histogram or bar graph for your Individual Data for Activity 2.

1. Determine the value of each of the following for your data set.

1. Mean

2. Median

3. Mode

4. Range

5. Interquartile Range

6. Standard Deviation

1. Record the combined class data for Activity 2 in the table below.

 Sum of the Numbers Rolled Frequency 2 3 4 5 6 7 8 9 10 11 12

1. Create a histogram or bar graph for the Class Data for Activity 2.

1. Determine the value of each of the following for the class data set.

1. Mean

2. Median

3. Mode

4. Range

5. Interquartile Range

6. Standard Deviation

What is Normal?

1. What terms can be used to describe the shape of a data distribution?

1. Make a sketch to illustrate each shape.

1. Provide a real world example of a data set that might produce each type of distribution.

1. What is a symmetric bell-shaped curve?

1. What is a normal curve?

1. What is the difference between a symmetric bell-shaped curve and a normal curve?

1. What is the Empirical Rule?

1. Label the provided Normal Curve to illustrate the Empirical Rule.

1. Assume that the data which reflects the “Heights of Women” is normally distributed.

Heights of Women
Mean = µ = 64.5 in.

Standard Deviation =σ = 2.5 in.

1. Label the provided normal curve to reflect this information.

1. What is the probability that a randomly selected woman would be 67 inches tall or taller? Explain how you determined your answer.

1. Shade the graph to reflect this information.

1. The population of walleye fish in a local lake is normally distributed.

Population of Walleye Fish

Mean = µ = 8 in.

Standard Deviation =σ = 0.6 in.

The game commission will only allow you to keep fish that are at least 7.4 inches long.

What percentage of the fish population can you keep from this lake? Label the provided normal curve to illustrate how you determined your answer.

Closure Questions

1. Do the percentages in each region stay the same on all normal curves? Explain your answer.

1. What is the total area under any normal curve?

1. Describe the differences in the shapes of normal curves used to represent two normally distributed data sets which have the same mean but different standard deviations.

1. Provide an example of a population which would probably be normally distributed. Justify your answer.

Normal Sketch Practice

In each problem: sketch, label, shade the region of the curve, and answer the question. The information in each question may not be accurate in real-life.

1. Music video artists are not the only ones that get to play around with money. The average salary for a music video producer is normally distributed with a mean of \$134,000 with a standard deviation of \$4,200. What percentage of music video producers make more than \$125,600?

2. A real estate agent, working entirely on commission, makes an average of \$850 with a standard deviation of \$260 weekly selling property in the city. If we assume this distribution is roughly normal, what is the probability that a real estate agent will make between \$1110 and \$1,630 selling property in the city?

3. Mr. Cerutti likes to collect random things, such as hotel bar soap. At one hotel, he found a 3.5oz bar of soap. Wholesale distributors report that the weight of hotel bar soap is normally distributed with a mean of 2.3oz and standard deviation of 0.4oz. How rare was this bar of soap? Hint: Find the area above that standard deviation!

4. The length it takes a teenager to respond to a Facebook update is (surprisingly) normally distributed with a mean of 4 hours and standard deviation of 23 minutes. What is the probability that a recorded time will not be in between 217 and 286 minutes?

DRAFT Maryland Common Core State Curriculum Lesson Plan for Algebra II August 2012 Page of