Podcast
Questions and Answers
What does the function normalcdf compute?
What does the function normalcdf compute?
How would you calculate the area to the right of a z-score using normalcdf?
How would you calculate the area to the right of a z-score using normalcdf?
For a normal distribution with a mean of 12 days and standard deviation of 3 days, how would you find the probability of exceeding 17 days?
For a normal distribution with a mean of 12 days and standard deviation of 3 days, how would you find the probability of exceeding 17 days?
What value does invNorm(0.08, 4.2, 0.65) return in the context of a toaster's lifespan?
What value does invNorm(0.08, 4.2, 0.65) return in the context of a toaster's lifespan?
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What does invNorm(0.99, 0, 1) help to determine in a standard normal distribution?
What does invNorm(0.99, 0, 1) help to determine in a standard normal distribution?
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When calculating the area to the left of a z-score, which bound should be used in normalcdf?
When calculating the area to the left of a z-score, which bound should be used in normalcdf?
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If a standard normal curve has 1% of its area to the right of a certain z-score, how can the z-score be calculated?
If a standard normal curve has 1% of its area to the right of a certain z-score, how can the z-score be calculated?
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Why are calculator answers from normalcdf generally more precise than z-score table answers?
Why are calculator answers from normalcdf generally more precise than z-score table answers?
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Study Notes
Normal Distribution and Graphing Calculator
- The graphing calculator function
normalcdfdetermines the area under a normal distribution curve between two z-scores or raw x-values. -
normalcdffinds the area to the left of each z-score and subtracts the left area of the lower z-score from the left area of the upper z-score. - Use
10^99as a large upper bound to find the area to the right of a z-score. - Use
-10^99as a large lower bound to find the area to the left of a z-score. - Calculator answers are generally more precise than z-score table answers.
Using normalcdf to Calculate Probabilities
-
Example 1:
- For a standard normal distribution, the probability between -0.85 and 2.31 is 0.792, calculated with
normalcdf(-0.85, 2.31, 0, 1).
- For a standard normal distribution, the probability between -0.85 and 2.31 is 0.792, calculated with
-
Example 2:
- For a flu duration with a mean of 12 days and standard deviation of 3 days, the probability of duration exceeding 17 days is 0.05, found using
normalcdf(17, 10^99, 12, 3).
- For a flu duration with a mean of 12 days and standard deviation of 3 days, the probability of duration exceeding 17 days is 0.05, found using
-
Example 3:
- For package delivery with a mean of 21 days and standard deviation of 5 days, the probability of delivery taking less than 15 days is 0.12, calculated with
normalcdf(-10^99, 15, 21, 5).
- For package delivery with a mean of 21 days and standard deviation of 5 days, the probability of delivery taking less than 15 days is 0.12, calculated with
Using invNorm to Calculate Data Values Given Area
- The
invNormfunction finds the data value corresponding to a given area to the left of that value in a normal distribution. -
Example 1:
- For toasters with a mean lifespan of 4.2 years and a standard deviation of 0.65 years, the warranty period to ensure no more than 8% replacement is 3.28 years (found with
invNorm(0.08, 4.2, 0.65)). A 3-year warranty is recommended.
- For toasters with a mean lifespan of 4.2 years and a standard deviation of 0.65 years, the warranty period to ensure no more than 8% replacement is 3.28 years (found with
-
Example 2:
- For a standard normal distribution, the z-score with 1% of the data above it is 2.33 (calculated using
invNorm(0.99, 0, 1)).
- For a standard normal distribution, the z-score with 1% of the data above it is 2.33 (calculated using
-
Example 3:
- For a standard normal curve, if 1% of the area lies to the right of a certain z-score, the z-score is 2.33 (calculated with
invNorm(0.01, 0, 1)orinvNorm(0.99, 0, 1))
- For a standard normal curve, if 1% of the area lies to the right of a certain z-score, the z-score is 2.33 (calculated with
Remember
- Ensure correct mean and standard deviation values are used in
normalcdfandinvNorm. - For
invNorm, consider the appropriate tail (left, right, or center) based on the problem's context.
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Description
This quiz covers the use of the normalcdf function on a graphing calculator for calculating areas under the normal distribution curve. It includes examples of probability calculations and tips for determining areas to the left and right of z-scores. Enhance your understanding of normal distribution with practical calculator techniques.
