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Empirical rule exercise, Exercises of Mathematics

Mathematics

Just a cheat sheet for the empirical rule

Typology: Exercises

2023/2024

Uploaded on 10/05/2024

alexis-smith-10
alexis-smith-10 🇺🇸

4 documents

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bg1
Statistics
Name:___________________________ Teacher:_______________
Block:______
689599.7PracticeWorksheet
Usethe689599.7Ruletoapproximateeachofthefollowing.
Usingthevaluesgiven,labeleachnormalcurvewiththenumericalvaluesforμ,μ±σ,μ±2σ
andμ±3σ.
1. Ratweightsarenormallydistributedwithμ=6lbs.andσ=0.45lbs.,X=N(6,0.45).
a. Findthepercentageofratsthatarelessthan6lbs.___________
b. Findthepercentageofratsthatarelessthan6.9lbs.___________
c. Findthepercentageofratsthatfallbetween5.1and6.9lbs.___________
d. Findthepercentageofratsthatareheavierthan6.45lbs.___________
e. Findthepercentageofratsthatareheavierthan8lbs.___________
For#2–8:ThemeanweightofadultAmericanmenis180poundswithstandarddeviationof
25pounds.Theweightsareapproximatelynormallydistributed.
2. Labelthecurve.
3. WhatpercentofalladultAmericanmenhaveaweightlessthan130pounds?
___________
4. WhatpercentofalladultAmericanmenhaveaweightbetween130and205pounds?
___________
5. WhatpercentofalladultAmericanmenhaveaweightlessthan230pounds?
___________
pf2

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Download Empirical rule exercise and more Exercises Mathematics in PDF only on Docsity!

Statistics Name: ___________________________ Teacher: _______________ Block: ______

68 95 99.7 Practice Worksheet Use the 68 95 99.7 Rule to approximate each of the following. Using the values given, label each normal curve with the numerical values for μ, μ ± σ, μ ± 2σ and μ ± 3σ.

  1. Rat weights are normally distributed with μ = 6 lbs. and σ = 0.45 lbs., X = N (6, 0.45).

a. Find the percentage of rats that are less than 6 lbs. ___________

b. Find the percentage of rats that are less than 6.9 lbs. ___________

c. Find the percentage of rats that fall between 5.1 and 6.9 lbs. ___________

d. Find the percentage of rats that are heavier than 6.45 lbs. ___________

e. Find the percentage of rats that are heavier than 8 lbs. ___________

For #2 – 8: The mean weight of adult American men is 180 pounds with standard deviation of 25 pounds. The weights are approximately normally distributed.

  1. Label the curve.
  2. What percent of all adult American men have a weight less than 130 pounds?
  3. What percent of all adult American men have a weight between 130 and 205 pounds?
  4. What percent of all adult American men have a weight less than 230 pounds?

Statistics Name: ___________________________ Teacher: _______________ Block: ______

  1. What percent of all adult American men have a weight less than 105 pounds?
  2. The heaviest 16% of all men in weight weigh more than how many pounds?
  3. What weight separates the lowest 2.5% of all American men in weight from the remaining weights? ___________

For #9 –16: Elephants have the longest pregnancy of all mammals. One species of elephant has a mean gestation period of 525 days and standard deviation of 32 days. Pregnancy length follows an approximately normal distribution.

  1. Label the curve.
  2. The longest 16% of all elephant pregnancies last at least how many days? ___________
  3. The middle 68% of all elephant pregnancies last between ________ and ________days.
  4. Only 2.5% of all elephant pregnancies last longer than ________ days.
  5. What percent of elephant pregnancies last less than 461 days? ________
  6. What percent of elephant pregnancies last between 525 and 557 days? ________
  7. What percent of elephant pregnancies last between 493 and 589 days? ________
  8. What percent of elephant pregnancies last less than 557 days? ________
  9. Maria received a 75% on her Government test and an 83% on her Algebra 2 test. The mean grade on the Government test was 72% with a standard deviation of 5%. The average grade on the Algebra 2 test was 81% with a standard deviation of 4%. On which test did Maria do better? Justify your answer.