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[AP Statistics] 2.2b Finding Areas in Normal Distributions

Last updated 5 months ago
16 questions

Areas under the normal distribution

1

Bartolo's 1st inning fastballs in 2016 had a mean speed of µ = 89.4 mph. His pitch speeds were normally distributed, with σ = 1.7 mph.

What percent of Bartolo's pitches were FASTER than the Miami Miracle pitch (85.7 mph)?




We want the area under the curve to the RIGHT of 85.7

On your calculator:
1. Press 2nd-Vars (DISTR)
2. Choose Normalcdf( (make sure you choose CDF not PDF)
3. Your calculator will ask for the follow 4 things:
  • Lower Bound - The lower bound for the portion of the curve that we want the area for should be 85.7
  • Upper Bound - Because we want EVERYTHING above 85.7, our upper bound should be a very large number. Usually I pick something like 10000.
  • Mean - The mean of this distribution is 89.4
  • Standard Deviation - The Standard Deviation of this distribution is 1.7
4. Choose "Paste" and hit enter twice.

The number it gives you is the area under the density curve from your lower bound to your upper bound. Always check with your intuition to make sure this number seems reasonable. Remember that we estimated this number earlier.

Also remember to answer the question with a sentence: What percent of Bartolo's pitches were FASTER than the Miami Miracle pitch (85.7 mph)?

1

Use your calculator to find the percentile for an adult women who is 58 inches tall.

Mean=64.5
SD = 2.5

1

What percent of adult women are between 63 and 66 inches tall?

Mean=64.5
SD = 2.5

1

If an adult woman is at the 20th percentile of height, how tall is she?

•Press 2nd-> Vars (DIST)
•Choose invNorm(
•Pick the area to the LEFT that you want to find (leave tail on LEFT)
Note: The area must be a number between 0 and 1. If you want an area of 20%, use 0.20
•Enter the Mean and SD
•Paste and then hit Enter
Use this to find the exact height that is at the 20th percentile.

1

Modify the procedure above to find the height of an adult woman who is SHORTER than 30% of adult women.

The questions that follow are from the textbook (Section 2-2). I'll mostly post odd questions so you can find the answers in the back of the book.
1

The weights of 9-ounce bags of a particular brand of potato chips can be modeled by a Normal distribution with mean 9.12 ounces and standard deviation 0.05 ounces

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Are there any problems above that you would like to go over in class? Indicate the question numbers below (Numbers refer to the Formative question number). I'll try to cover anything that is highly requested.