For a normal population with known variance ?2 , answer

QUESTION:

For a normal population with known variance \(\sigma^{2}\), answer the following questions:

(a) What is the confidence level for the interval \(\bar{x}-2.14 \sigma / \sqrt{n} \leq \mu \leq \bar{x}+2.14 \sigma / \sqrt{n}\)?

(b) What is the confidence level for the interval \(\bar{x}-2.49 \sigma / \sqrt{n} \bar{x}-2.49 \sigma / \sqrt{n} \leq \mu \leq \bar{x}+2.49 \sigma / \sqrt{n}\)?

(c) What is the confidence level for the interval \(\bar{x}-1.85 \sigma / \sqrt{n} \leq \mu \leq \bar{x}+1.85 \sigma / \sqrt{n}\)?

(d) What is the confidence level for the interval \(\mu \leq \bar{x}+2.00 \sigma / \sqrt{n}\)?

(e) What is the confidence level for the interval \(\bar{x}-1.96 \sigma / \sqrt{n} \leq \mu\)?

Equation Transcription:

Text Transcription:

sigma^2

x bar-2.14sigma/sqrt n </= mu </= x bar +2.14sigma/sqrt n

x bar-2.49sigma/sqrt n x bar-2.49sigma/sqrt n </= mu </= x bar +2.49/sqrt n

x bar-1.85sigma/sqrt n </= mu </= x+1.85sigma/sqrt n

mu </= x bar+2.00 sigma/sqrt n

x bar-1.96sigma/sqrt n </= mu