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

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%.

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%.

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.

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.

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.

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?

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%:

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:

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:

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: