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Statistics exam scores are normally distributed with a known population standard deviation of three points. A random sample of 36 scores gives x-bar = 68. For a 90% confidence level, what z-score is used to compute the error bound?
A1.960
B2.326
C0.900
D1.645
Answer & Solution
Correct answer: D. 1.645
1. For CL = 0.90, α = 1 - 0.90 = 0.10, so α/2 = 0.05.
2. The needed z-score is z(0.05), the value with area 0.05 to its right on the standard normal curve.
3. Using invNorm(0.95, 0, 1), z(0.05) = 1.645.
4. Option A is the z-score for a 95% confidence level and option C is for 98%, not 90%.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 8 "Confidence Intervals", section 8.1 A Single Population Mean using the Normal Distribution_
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