Elena wants to build a one-sample $$ z $$ interval to estimate what proportion of computers produced at a factory have a certain defect. She chooses a confidence level of $$ 94 \% $$. A random sample of 200 computers shows that 12 computers have the defect. What critical value $$ z^{*} $$ should Elena use to construct this confidence interval? Choose 1 answer: (A) $$ z^{*}=1.55 $$ (B) $$ z^{*}=1.75 $$ (C) $$ z^{*}=1.88 $$ (D) $$ z^{*}=1.96 $$

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To determine the appropriate critical value for a 94% confidence level, we first note that the total area in both tails is 6% (since 100% - 94% = 6%). Since the distribution is symmetric, each tail has 3% (0.03) of the area. We need the z-value such that 97% (1 - 0.03) of the distribution is to the left of it.

Looking up the z-value for a cumulative probability of 0.97 (or using a calculator), we find that approximately:

z* ≈ 1.88

Thus, the correct answer is (C) z* = 1.88.
Elena should use $$ z^{*} = 1.88 $$ to construct the confidence interval.

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