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Lesson 5.7 Practice: Calculating a Data value from a given area cloned 2/23/2023

Last updated over 1 year ago
12 questions
Note from the author:
Get out your notes for 5.7. You only need a calculator and the Normal Distribution Chart.
Get out your notes for 5.7. You only need a calculator and the Normal Distribution Chart.
Required
8

Given the model N(125, 15), draw the Normal Model, clearly label it with the z-score cutpoints, give the corresponding data values and show the % that the 68-95-99.7 Rule gives in each section.
Use the 'show your work' area.

Required
2
Using the Normal Distribution Model from #1:
What is the z-score for the lower 2.5%? _______
Give the corresponding data value cutpoint for the lower 2.5%. _______
Required
2
Using the Normal Distribution Model from #1:
What is the z-score for the upper 16%? _______
Give the corresponding data value cutpoint for the upper 16%. _______
Required
1

The Virginia Cooperative Extension reports that the mean weight of yearling Angus steers is 1152 pounds and the standard deviation is 84 pounds.

What is the notation for this normal distribution model? ex. N(...

Required
3
The Virginia Cooperative Extension reports that the mean weight of yearling Angus steers is 1152 pounds and the standard deviation is 84 pounds.

Using N(1152, 84) what is the cutpoint data value for the lowest 20% of weights?
First: what is the decimal area we are interested in? _______

Second: what is the corresponding z-score to the lowest 20%? _______

Third: Set up the z-score formula and calculate the data value for the steer's weight.
Steer's weight = _______ do not include units, round to two places.
Required
3
The Virginia Cooperative Extension reports that the mean weight of yearling Angus steers is 1152 pounds and the standard deviation is 84 pounds.

Using N(1152, 84) what is the cutpoint data value for the lowest 8% of weights?
First: what is the decimal area we are interested in? _______

Second: what is the corresponding z-score to the lowest 8%? _______

Third: Set up the z-score formula and calculate the data value for the steer's weight.
Steer's weight = _______ do not include units, round to two places.
Required
3
The Virginia Cooperative Extension reports that the mean weight of yearling Angus steers is 1152 pounds and the standard deviation is 84 pounds.

Using N(1152, 84) what is the cutpoint data value for the lowest 75% of weights?
First: what is the decimal area we are interested in? _______

Second: what is the corresponding z-score to the lowest 75%? _______

Third: Set up the z-score formula and calculate the data value for the steer's weight.
Steer's weight = _______ do not include units, round to two places.
Required
3
The Virginia Cooperative Extension reports that the mean weight of yearling Angus steers is 1152 pounds and the standard deviation is 84 pounds.
Using N(1152, 84) for the Angus steers, what is the cutpoint data value where you would expect to find the highest 10% of weights?
REMEMBER: the Normal Distribution chart ONLY gives the area to the LEFT of a data value, you will need to subtract from 100 first!!!

What area are we looking for on the Normal Distribution Chart in order to find the top 10%?_______
What z-score corresponds to this area? _______
What data value for steer weight corresponds to this z-score? _______
Required
3
The Virginia Cooperative Extension reports that the mean weight of yearling Angus steers is 1152 pounds and the standard deviation is 84 pounds.
Using N(1152, 84) for the Angus steers, what weight would give the cutpoint for the top 4%?

What area are we interested? (refer to #8 if you aren't sure) _______
Using the Normal Distribution Chart, what z-score corresponds to this area? _______
Set up the z-score formula and calculate the steer weight that would be at the top 4%: _______
Required
3
The Virginia Cooperative Extension reports that the mean weight of yearling Angus steers is 1152 pounds and the standard deviation is 84 pounds.
Using N(1152, 84) for the Angus steers, what weight represents the 40th percentile?
Remember 'percentile means the area to the LEFT'.

What is the area we are interested in? _______
Check the Normal Distribution chart, what z-score corresponds to this area? _______
Use this z-score to calculate the data value for the steer weight at this point: _______
Required
3
The Virginia Cooperative Extension reports that the mean weight of yearling Angus steers is 1152 pounds and the standard deviation is 84 pounds.
Using N(1152, 84) for the Angus steers, what weight represents the 99th percentile?
Remember 'percentile means the area to the LEFT'.

What is the area we are interested in? _______
Check the Normal Distribution chart, what z-score corresponds to this area? _______
Use this z-score to calculate the data value for the steer weight at this point: _______
Required
7
Find the IQR of Angus Steer weights: using N(1152, 84) for the Angus steers, what are the cutpoint values for the central 50%?
First: what are the % as decimals for Q1 _______ AND Q3 _______

Second: what is the z-score that corresponds to Q1? _______
what is the z-score that corresponds to Q3? _______

Third: calculate the steer weight at Q1: _______
calculate the steer weight at Q3: _______

Fourth: NOW find the IQR using the two weights: _______