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Assuming a normal distribution, find the limitsμ±hfor a 90%confidence interval; for a 95%confidence interval; for a 99%confidence interval. What percent confidence interval isμ±1.3σ?Hints: See Section8, Example3, and Problems,8.7,8.22 and8.23.

Short Answer

Expert verified

The upper and lower limits are mentioned below:

μ±1.645σμ±1.96σμ±2.579σ

And percent confidence interval,

I=82.5%

Step by step solution

01

Given Information

The value of mean and standard deviation.

μ=0σ=1

02

Definition of Binomial Distribution.

The expected value (also known as expectation) is a generalisation of the weighted average in probability theory.

03

Calculate upper and lower limits for total area of 0.9. 

Calculate limits for confidence interval of90%.

h=1.645μ−1.645σμ+1.645σ

04

Calculate upper and lower limits for total area of 0.95. 

Calculate limits for confidence interval of95%.

h=1.96μ−1.96σμ+1.96σ

05

Calculate upper and lower limits for total area of 0.99.

Calculate limits for confidence interval of99%.

h=2.579μ−2.579σμ+2.579σ

06

Calculate percent confidence interval. 

Use conditions,

μ=0σ=1h=1.36μ±1.36σ

Calculate percent confidence interval.

I=82.5%

Hence, the upper and lower limits are mentioned below:

μ±1.645σμ±1.96σμ±2.579σ

And percent confidence interval,

I=82.5%

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