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 in. If her cuts are normally distributed, what percentage of her squares would be between 4.9 and 5.1 in?

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 [tex]\implies \boxed{68\%}[/tex].

*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.

mhanifa mhanifa · Answer 2 · 2021-06-13T20:31:31+02:00

mhanifa mhanifa

13-06-2021

Answer:

68.26%

Step-by-step explanation:

Given:

Mean μ = 5 in
Standard deviation σ = 0.1 in

The squares between 4.9 and 5.1 represent:

x = 5 ± 0.1

Relevant z- scores are:

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

From the z-score table we get:

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

The data between these points is:

84.13% - 15.87% = 68.26%

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