Lesson 5.6 Normal Distribution Calculations Due 2/21 11:55 pm

Instructions

Get out your 68-95-99.7 Rule half sheets and your packet: Lesson 5.5 & 5.6.
No statsmedic today, only the calculator and the Normal Distribution Chart.

Required

1

What does the z-score mean?
Suppose that a Normal model described student scores in a history class.
Francisco has a standardized score (z-score) of +2.5.

This means that Francisco’s score...

8

The distribution of speed follows an approximately Normal distribution with a mean of 80 mph and a standard deviation of 7.7 mph.
Use the 'show your work' section to put in the Delorean speeds under the axis for the Normal Distribution Model.
Then answer:
What speed is 2 standard deviations above the mean?
Be sure to include units 'mph' in your answer.
I will check your normal curve data values, points will be subtracted if it is not correct.

Required

1

Give the notation for the Normal model using the Delorean Speed information above.
Use the format: N(#, #)

Required

2

Using the 68-95-99.7 Rule & your half sheet:
What percent of the runs will give the Delorean a speed greater than 87.7 mph?

THEN shade in the probability area you are calculating in the 'show your work area'.
1 point is for your shading.

Required

2

Using the 68-95-99.7 Rule & your flip book:
What percent of the runs will give the Delorean a speed between 64.6 mph and 87.7 mph?

THEN Shade in the probability area that you are calculating in the 'show your work' area.
1 point is for your shading.

Required

3

What percent of the runs will give the Delorean a speed less than 68.45 mph?
First: what is the z-score for 68.45? _______  Enter all decimal places for this one.
Use the z-score formula: 


Second: answer,
what is the proportion of runs that will give the Delorean a speed less than 68.45 mph? _______  Include four places past the decimal or as a percent.

THEN: Shade in the probability area that you are calculating in the 'show your work' area.
1 point is for your shading.

Required

5

What percent of the runs will give the Delorean a speed greater than 85 mph?
First: what is the z-score for the speed? _______ 
Remember to round to two places.



Second: be careful, I am asking for the percent GREATER than 85 mph, think about what you need to do, collaborate! 
What is the proportion of speeds less than 85 mph? _______ 
              
Third: What do you need to do with the value to find the proportion higher?
                                                      Enter:  add, subtract, multiply or divide _______ 

           What percent of the runs will give the Delorean a speed greater than 85 mph? _______ 
        Hint: the area to the left and the right need to add to 1.0, the total area under the curve.
THEN: Shade in the probability area that you are calculating in the 'show your work' area.
1 point is for your shading.

Required

7

What percent of the runs will give the Delorean a speed between 70 and 95 mph?
First: what is the z-score for the speed of 70 mph? _______   
Remember to round to two places.
          what is the z-score for the speed of 95 mph? _______ 



Second: what proportion corresponds to 70 mph? _______ 
               what proportion corresponds to 95 mph? _______ 

Third: answer, what will you do with the two proportions? 
Hint: you want the area BETWEEN the two points, check your notes for what you need to do if you can't remember.
                     Enter: add, subtract, multiply or divide  _______ 
What percent of the runs will give the Delorean a speed between 70 and 95 mph? _______ 
THEN: Shade in the probability area that you are calculating in the 'show your work' area.
1 point is for shading under the curve.

Required

1

High levels of cholesterol in the blood increase the risk of heart disease.
For teenage boys, the distribution of blood cholesterol is approximately normal with
mean μ = 151.6 milligrams of cholesterol per deciliter of blood (mg/dl) and
standard deviation σ = 25 mg/dl.

What is the Normal model for this situation?
Use the format: N(#, #)

Required

3

What proportion of teen boys have cholesterol levels less than 100 mg/dl?
First: what is the z-score for 100 mg/dl? _______  Remember to round to two places.
                       
Second: What is the proportion? _______ 

THEN:  Shade in the probability area that you are calculating in the 'show your work' area.
1 point is for shading under the curve.

Required

5

Cholesterol levels of 200 or higher are considered high for teenagers. 
What percent of teen boys have high cholesterol?
First: what is the z-score for 200 mg/dl? _______ 



Second: What is the proportion to the left of the z-score? _______ 
               What do you need to do with the value to find the proportion higher?
                  Enter: add, subtract, multiply or divide  _______ 
Third: what is the proportion GREATER than 200 mg/dl? _______ 

THEN: Shade in the probability area that you are calculating in the 'show your work' area.
1 point is for shading under the curve.

Required

7

Cholesterol levels between 170 mg/dl and 200 mg/dl are considered borderline high for teenagers. What percent of teen boys have borderline high cholesterol levels?
First: what is the z-score for 170 mg/dl?  _______ 
          what is the z-score for 200 mg/dl?  _______ 


Second: What is the proportion to the left of 170?  _______ 
               What is the proportion to the left of 200?  _______ 

Third: what will you do with the two proportions? 
Enter: add, subtract, multiply or divide _______ 
            What percent of teen boys have borderline high cholesterol levels? _______ 

THEN: Shade in the probability area that you are calculating in the 'show your work' area.
1 point is for shading under the curve.

Required

2

6th grade STAAR scores were tabulated for Round Rock ISD, the normal model N(1142, 110) was appropriate for the data.
What is the mean? _______ 
What is the standard deviation? _______ 

Required

1

6th grade STAAR scores were tabulated for Round Rock ISD, the normal model N(1142, 110) was appropriate for the data.
If a student scored 1040 on his STAAR test, what was his z-score?

Round your answer to three places past the decimal.

Required

2

6th grade STAAR scores were tabulated for Round Rock ISD, the normal model N(1142, 110) was appropriate for the data.
A student scored 1040 on his STAAR test, you just calculated his z-score.
What does this mean?

Required

3

What does the z-score mean?Suppose that a Normal model described student scores in a history class. Francisco has a standardized score (z-score) of +2.5. This means that Francisco’s score...

Give the notation for the Normal model using the Delorean Speed information above.Use the format: N(#, #)

Using the 68-95-99.7 Rule & your half sheet:What percent of the runs will give the Delorean a speed greater than 87.7 mph?THEN shade in the probability area you are calculating in the 'show your work area'.1 point is for your shading.

Using the 68-95-99.7 Rule & your flip book:What percent of the runs will give the Delorean a speed between 64.6 mph and 87.7 mph?THEN Shade in the probability area that you are calculating in the 'show your work' area.1 point is for your shading.

6th grade STAAR scores were tabulated for Round Rock ISD, the normal model N(1142, 110) was appropriate for the data.If a student scored 1040 on his STAAR test, what was his z-score?Round your answer to three places past the decimal.

6th grade STAAR scores were tabulated for Round Rock ISD, the normal model N(1142, 110) was appropriate for the data.A student scored 1040 on his STAAR test, you just calculated his z-score. What does this mean?

Using the normal model: N(1142, 110)Which 6th grade STAAR score is more unusual: a score of 889 or 1351?Hint: use the z-scores to compare

What does the z-score mean?
Suppose that a Normal model described student scores in a history class.
Francisco has a standardized score (z-score) of +2.5.

This means that Francisco’s score...

Give the notation for the Normal model using the Delorean Speed information above.
Use the format: N(#, #)

Using the 68-95-99.7 Rule & your half sheet:
What percent of the runs will give the Delorean a speed greater than 87.7 mph?

THEN shade in the probability area you are calculating in the 'show your work area'.
1 point is for your shading.

Using the 68-95-99.7 Rule & your flip book:
What percent of the runs will give the Delorean a speed between 64.6 mph and 87.7 mph?

THEN Shade in the probability area that you are calculating in the 'show your work' area.
1 point is for your shading.

6th grade STAAR scores were tabulated for Round Rock ISD, the normal model N(1142, 110) was appropriate for the data.
If a student scored 1040 on his STAAR test, what was his z-score?

Round your answer to three places past the decimal.

6th grade STAAR scores were tabulated for Round Rock ISD, the normal model N(1142, 110) was appropriate for the data.
A student scored 1040 on his STAAR test, you just calculated his z-score.
What does this mean?

Using the normal model: N(1142, 110)
Which 6th grade STAAR score is more unusual: a score of 889 or 1351?

Hint: use the z-scores to compare