27.80% is percentage of items .
What percentage means?
Mean = 7
standard deviation = 3 ounces
Required % = p (5.6<x < 7.1 ) × 100 = ?
z = x - μ/σ = 5.6 - 7/2
z = 7.1 - 7/2 = 0.05
∴ P(5.6 < x < 7.1 ) = p ( - 0.7 < z < 0.05 )
p( z < 0.05 ) - p ( z < - 0.7)
= 0.51994 - 0.24196 ≅ 0.2780
So, required % = 0.2780 × 100
= 27.80%
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