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Amanda [17]
3 years ago
14

Tori is cutting fabric squares to make a quilt. Her squares on average are 5 in. on each side with a standard deviation of 0.1 i

n. If her cuts are normally distributed, what percentage of her squares would be between 4.9 and 5.1 in?
Mathematics
2 answers:
lapo4ka [179]3 years ago
5 0

Answer:

\approx 68\%

Step-by-step explanation:

For normal distributions only, all data falls within approximately 68% of one standard deviation, 95% of two standard deviations, and close to 100% of three standard deviations. The standard deviation is far too small to represent two or three standard deviations, hence \implies \boxed{68\%}.

*Important: This problem would be unsolvable if the question did not say her cuts were normally distributed, because the information above is only applicable to normal distributions.

babymother [125]3 years ago
4 0

Answer:

  • 68.26%

Step-by-step explanation:

<u>Given:</u>

  • Mean μ = 5 in
  • Standard deviation σ = 0.1 in

<u>The squares between 4.9 and 5.1 represent:</u>

  • x = 5 ± 0.1

<u>Relevant z- scores are:</u>

  • z = (x - μ)/σ
  • z = (5.1 - 5)/0.1 = 1
  • z = (4.9 - 5)/0.1 = -1

<u>From the z-score table we get:</u>

  • z = 1 ⇒ 84.13% mark
  • z = -1 ⇒ 15.87% mark

<u>The data between these points is:</u>

  • 84.13% - 15.87% = 68.26%

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