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
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.

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 $$\displaystyle{n}={17}$$