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Construct the confidence intervals specified to estimate µ

50. Use the following information to construct the confidence intervals specified to estimate µ
a) 95% confidence; = 25, σ2 = 12.25, and n = 60.
b) 98% confidence; = 119.6, S2 = 570.7321, and n = 75.
c) 90% confidence; ∑X = 1814.4, σ2 = 0.948676, and n = 32.

51. A sample of size n = 10 is randomly selected from a normal population with mean µ = 52 and variance σ2 = 22.5. The sample value X-bar is calculated.
d) find P( > 55)
e) find P(50 ≤ ≤ 60)
f) find P( ≤ 55)

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See the attached file for complete solution. The text here may not be copied exactly as some of the symbols / tables may not print. Thanks

50. Use the following information to construct the confidence intervals specified to estimate µ
a) 95% confidence; = 25, σ2 = 12.25, and n = 60.

n>30 and σ2 known we will use z-value to construct the confidence interval. The value of z for 95% confidence is +/-1.96
Now calculate the standard error
Standard Error = σ/n0.5 = (12.25/60)^0.5=0.4518
Confidence interval = ...

Solution Summary

Illustrates in simple steps in document file (no excel used) how to construct the confidence intervals and calculate the probabilities for mean of a normal distribution.

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