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a survey found that the american family generates an average of 17.2 pounds of glass garbage...

a survey found that the american family generates an average of 17.2 pounds of glass garbage each year. Assume the standard deviation of the distribution is 2.5 pounds. Find the probability that the mean of a sample of 30 families will be between 16.4 and 17.4 pounds. The correction factor can be ignored

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Answer #1

Here, μ = 17.2, σ = 2.5/sqrt(30) = 0.4564, x1 = 16.4 and x2 = 17.4.
We need to compute P(16.4<= X <= 17.4). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z1 = (16.4 - 17.2)/0.4564 = -1.75
z2 = (17.4 - 17.2)/0.4564 = 0.44

Therefore, we get
P(16.4 <= X <= 17.4) = P((17.4 - 17.2)/0.4564) <= z <= (17.4 - 17.2)/0.4564)
= P(-1.75 <= z <= 0.44) = P(z <= 0.44) - P(z <= -1.75)
= 0.67 - 0.0401
= 0.6299

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