Question

Determine the sample size taken from a normal distribution N(M, 25) to get length of interval of 4 using 90\% confidence level for the mean.

Confidence intervals
asked 2021-08-07
Determine the sample size taken from a normal distribution N(M, 25) to get length of interval of 4 using \(\displaystyle{90}\%\) confidence level for the mean.

Answers (1)

2021-08-16

Step 1
Here we need to find the required sample size.
Step 2
Here it is given that the sample is taken from N(M,25).
Here we need to determine the sample size.
We know \(\displaystyle{n}={\left({\frac{{{z}_{{\frac{\alpha}{{2}}}}\times{6}}}{{{E}}}}\right)}^{{{2}}}\).
At \(\displaystyle{90}\%\) confidence level \(\displaystyle{z}_{{\frac{\alpha}{{2}}}}={1.645}\)
Also, \(E=\frac{length}{2}=\frac{4}{2}=2, 6=5\)
\(\displaystyle\therefore{n}={\left({\frac{{{1.645}\times{5}}}{{{2}}}}\right)}^{{{2}}}={16.912}\)
\(\displaystyle\approx{17}\)
Sample size \(\displaystyle{n}={17}\)

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