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Lesson 5.6 Normal Distribution Calculations Practice cloned 2/21/2023

Last updated over 1 year ago
24 questions
Required
7

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.

Required
1

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

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1

Using the 68-95-99.7 Rule & your flip book:
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'.

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1

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.

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2
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? _______
Second: answer,
what is the proportion of runs that will give the Delorean a speed less than 68.45 mph? _______

THEN: Shade in the probability area that you are calculating in the 'show your work' area.
Required
2
What percent of the runs will give the Delorean a speed greater than 85 mph?
First: what is the z-score for the speed? _______
Second: answer,
What percent of the runs will give the Delorean a speed greater than 85 mph? _______

THEN: Shade in the probability area that you are calculating in the 'show your work' area.
Required
6
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? _______
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?
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.
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(mean, std. dev.)

Required
2
What proportion of teen boys have cholesterol levels less than 100 mg/dl?
First: what is the z-score for 100 mg/dl? _______
Second: What is the proportion? _______

THEN: Shade in the probability area that you are calculating in the 'show your work' area.
Required
4
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?
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.
Required
6
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? 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.
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
1

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?

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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...

Required
2
The heights of Dutch men have a mean of 184 cm and standard deviation of 8 cm.
Give the notation for the Normal model for the Dutch men: _______

The heights of French men have a mean of 174 cm and a standard deviation is 7.1 cm.
Give the notation for the Normal model for the French men: _______
Required
1

The heights of Dutch men have a mean of 184 cm and standard deviation of 8 cm.
The heights of French men have a mean of 174 cm and a standard deviation is 7.1 cm.

A French man is 194 cm tall and a Dutch man is 204 cm tall.

What is the z-score for the French man? (round to two places past the decimal point)

Required
1

The heights of Dutch men have a mean of 184 cm and standard deviation of 8 cm.
The heights of French men have a mean of 174 cm and a standard deviation is 7.1 cm.

A French man is 194 cm tall and a Dutch man is 204 cm tall.

What is the z-score for the Dutch man? (round to three places past the decimal point)

Required
2

The heights of Dutch men have a mean of 184 cm and standard deviation of 8 cm.
The heights of French men have a mean of 174 cm and a standard deviation is 7.1 cm.

Who is taller compared to males in their country, a French man who is 194 cm tall
or a Dutch man who is 204 cm tall?

How do you know? Explain clearly using what we have discussed in class about z-scores.

Required
2
The heights of Dutch men have a mean of 184 cm and standard deviation of 8 cm.

A Dutch man was 178.2 cm tall, what is his z-score? _______ remember to round z score to 2 places
What proportion of Dutch men is he taller than? _______
Required
2
The heights of Dutch men have a mean of 184 cm and standard deviation of 8 cm.

A Dutch man was 178.2 cm tall, what is his z-score? _______ remember to round z score to 2 places
What proportion of Dutch men is he taller than? _______
Required
5
The heights of Dutch men have a mean of 184 cm and standard deviation of 8 cm.

What is the probability of randomly choosing a Dutch man between 173.5 and 193.5 cm?
What is the z-score for 173.5 cm? _______ remember to round z score to 2 places
What is the z-score for 193.5 cm? _______ remember to round z-score to 2 places

What is the probability of choosing a Dutch man less than 173.5 cm? _______
What is the probability of choosing a Dutch man less than 193.5 cm? _______

What is the probability of randomly choosing a Dutch man between 173.5 and 193.5 cm? _______
Required
3
The heights of Dutch men have a mean of 184 cm and standard deviation of 8 cm.
What is the probability of randomly choosing a Dutch man over 203.8 cm tall?

First: What is the z-score for 203.8 cm? _______ remember to round z score to 2 places
Second: What is the probability of choosing a Dutch man 203.8 cm tall or less? _______
NOW: What is the probability of choosing a Dutch man over 203.8 cm tall? _______

(This is the same as 203.8 cm tall or more.)
Required
3

You just found the probability of randomly choosing a Dutch man over 203.8 cm tall.
Using the z-score and the probability, would you say this is an unusual height for a Dutch man?
Explain why or why not. Select both answers.