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Lesson 5.7: Calculate a Data value from Prob. due 2/22

Last updated over 1 year ago
10 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
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: Use the blue table to find the area closest to our area. Look up the z-score.
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: Use the blue table to find the area closest to our area. Look up the z-score.
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 75th percentile of weights?
First: what is the decimal area we are interested in? _______

Second: Use the blue table to find the area closest to our area. Look up the z-score.
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!!!

First: What area are we looking for on the Normal Distribution Chart in order to find the top 10%?_______ Remember, the chart ONLY shows the area to the left.
Second: Use the blue table to find the area closest to our area. Look up the z-score.
What z-score corresponds to this area? _______
Third: 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%?

First: What area are we interested? (refer to #5 if you aren't sure) _______
Second: Use the blue table to find the area closest to our area. Look up the z-score.
What z-score corresponds to this area? _______
Third: 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'.

First: What is the proportion area we are interested in? _______
Second: Check the z chart, what z-score corresponds to this area? _______
Third: Use this z-score to calculate the data value for the steer weight at this point: _______
Required
3
Review of finding a percentile (Lesson 5.6)
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 would be the percentile for a steer weighing in at 1394.76 pounds?
Remember 'percentile means the area to the LEFT'.

First: What is the z score for this weight? _______
Second: Check the z chart, what area corresponds to this z score? _______
Third: Would at steer at this weight be unusual? Yes or No _______
Required
3
Review of finding a percentile (Lesson 5.6)
The Virginia Cooperative Extension reports that the mean weight of yearling Brahman bull is 2078 pounds and the standard deviation is 103 pounds.
Using N(2078, 103) for the Brahman bulls, what would be the percentile for a bull weighing in at 2367.43 pounds?
Remember 'percentile means the area to the LEFT'.

First: What is the z score for this weight? _______
Second: Check the z chart, what area corresponds to this z score? _______
Third: Would at steer at this weight be unusual? Yes or No _______
Required
3

Compare the Angus steer and the Brahman bull from #8 and #9.
a. Which is more unusual?
b. Why?