a)
Here, μ = 8, σ = 0.1, x1 = 7.8 and x2 = 8.17. We need to compute P(7.8<= X <= 8.17). The corresponding z-value is calculated using Central Limit Theorem
z = (x - μ)/σ
z1 = (7.8 - 8)/0.1 = -2
z2 = (8.17 - 8)/0.1 = 1.7
Therefore, we get
P(7.8 <= X <= 8.17) = P((8.17 - 8)/0.1) <= z <= (8.17 -
8)/0.1)
= P(-2 <= z <= 1.7) = P(z <= 1.7) - P(z <= -2)
= 0.9554 - 0.0228
= 0.9326
b)
-1.91 = (x - 8)/0.1
x = 0.1 * -1.91 + 8
x = 7.809
(2 points) The distribution of actual weights of 8-oz chocolate bars produced by a certain machine...
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