The mean of the sample is x-bar is determined to be 59.2 and population standard deviation, σ, is known to be 3.8. The 90% confidence interval about μ if the sample size, n, is 45 be 58.27< μ<60.13
A simple random sample of size n is drawn from a population whose population standard deviation, σ, is known to be 3.8. The sample mean, x-bar, is determined to be 59.2.
Hence,
n=45
σ=3.8
x-bar=59.2
The z value for the 90% confidence interval is z=1.645.
Then, μ=(x-bar)±(z×σ/[tex]\sqrt{n}[/tex])
μ=59.2±(1.645×3.8/[tex]\sqrt{45}[/tex])
μ=59.2±0.9318
59.2-0.9318<μ<59.2+0.9318
58.27< μ<60.13
Therefore, The 90% confidence interval about μ if the sample size, n, is 45 be 58.27< μ<60.13
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