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Lesson 5.5 Part 2: using the 68-96-99.7 Rule Due 2/14

Last updated over 1 year ago
17 questions
Required
11

A new group of IQ tests are standardized to a Normal Model, N(110,14). Draw a model for these IQ scores in the show your work area. 1. use the textbox tool to insert the data values at the correct tic marks (std dev marks)
2. Clearly label the normal model with dashed horizontal lines and arrows to show the 68-95-99.7 Rule on the normal curve in the show your work area. (you can also use shading to show the different percentages) The first one has been done for you.

Also answer:
What percent of the data values fall between the IQ's of 96 and 124?

Note: 10 of the points for this problem come from the 'show your work' section, I will grade this portion.

Required
2

Using the Normal Distribution in #1:
What % of the IQ scores are above 110?
Answer as a percent and include the correct symbol (%)

Then shade the correct area in the 'show your work' section.

Required
5
Use the normal distribution from #1:
Between what z-scores (# of std dev from the mean) would you expect the central 95% of IQ scores to be found?
Lower: _______ Upper: _______

Between what IQ scores would the central 95% be found?
Lower: _______ Upper: _______

Now shade the area in the show your work section.
Required
5
Use the normal distribution from #1:
Between what z-scores (# of std dev from the mean) would you expect the central 68% of IQ scores to be found?
Lower: _______ Upper: _______

Between what IQ scores would the central 68% be found?
Lower: _______ Upper: _______

Then shade the corresponding area under the normal curve in the 'show your work' section below.
Required
5
Use the normal distribution from #1:
Between what z-scores (# of std dev from the mean) would you expect the central 99.7% of IQ scores to be found?
Lower: _______ Upper: _______

Between what IQ scores would the central 99.7% be found?
Lower: _______ Upper: _______

Then shade the corresponding area under the normal curve in the 'show your work' section below.
Required
3
Using the Normal Distribution in #1:
What is the z-score for the lower 16% of the IQ scores (the 16th percentile)? _______

What IQ score is the 16th percentile? _______

Then shade the corresponding area under the normal curve in the 'show your work' area below.
Required
4
Using the Normal Distribution from #1:
How many standard deviations is the top 2.5% from the mean? _______

What is the IQ score needed to be in the top 2.5%? _______

What percentile would this be? _______
Hint: remember, percentiles are the percent to the LEFT of a given point

Then shade the corresponding area under the normal curve in the 'show your work' area below,.
Required
4
Using the Normal Distribution from #1:
How many standard deviations from the mean is the top 16% of the IQ scores? _______

What is the IQ score needed to be in the top 16%? _______

What percentile would this be? _______
Hint: remember, percentiles are the percent to the LEFT of a given point

Then shade the corresponding area under the normal curve in the 'show your work' area below.
Required
3
Using the Normal Distribution from #1:
What is the percentile of an IQ score of 82? _______

What is the percentile of an IQ score of 124? _______

What is the percentile of an IQ score of 68? _______
Hint: remember, percentiles are the percent to the LEFT of a given point
Required
2
Fill in the blanks:
Using the normal distribution model:
N(110, 14) Mean= _______ Standard Deviation= _______
Required
2
Fill in the blanks:
Using the normal distribution model:
N(27.5, 3.6) Mean= _______ Standard Deviation= _______
Required
2
Fill in the blanks:
Using the normal distribution model:
N(375, 42.3) Mean= _______ Standard Deviation= _______
Required
1

Use your Normal Distribution half sheet:
What percent of the data is between one standard deviation below the mean and 2 standard deviations above the mean?

Check the shaded area in the show your work section. Enter your answer as a percent, use the symbol.
Shade part of the shaded region so your answer will be marked correct.

Required
1

Use your Normal Distribution half sheet:
What percent of the data is between the two points at: two standard deviation below the mean and the mean?

Check the shaded area in the show your work section. Enter your answer as a percent, use the symbol.
Shade part of the shaded region so your answer will be marked correct.

Required
1

Use your Normal Distribution half sheet:
What percent of the data is between the points: two standard deviation below the mean and one standard deviations above the mean?

Check the shaded area in the show your work section. No work needed by you. Enter your answer as a percent, use the symbol.
Shade part of the shaded region so your answer will be marked correct.

Required
5
Using the Normal Model: N(151.7, 5.6) what is the mean? _______
what is the standard deviation? _______

What is the z-score for the data value of 144?
Hint:

Set up your work and calculate your answer. z-score = _______
Make sure to include the sign if it is negative. Include three places past the decimal.

What is the z-score for the data value of 160? z-score = _______
Round to three places past the decimal.

Which data value is more extreme? (z-score is further away from zero?) _______
Enter the data value as your answer.
Required
5
Using the Normal Model: N(2.3, 0.8) what is the mean? _______
what is the standard deviation? _______

What is the z-score for the data value of 3.2?
Hint:

Set up your work and calculate your answer. z-score = _______
Include three places past the decimal.

What is the z-score for the data value of 1.6? z-score = _______
Round to three places past the decimal. Make sure to include the sign if it is negative.

Which data value is more extreme(unusual)? (z-score is further away from zero?) _______
Enter the data value as your answer.