Answer :
Answer:
The sample size should be approximately 151.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 100
Population standard deviation, σ = 15
We have to evaluate the sample size, n.
Alpha, α = 0.10
Confidence interval:
[tex]\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}[/tex]
Putting the values, we get,
[tex]z_{critical}\text{ at}~\alpha_{0.10} = \pm 1.64[/tex]
[tex]100 \pm 1.64(\frac{15}{\sqrt{n}} ) = (98,102)[/tex]
[tex]100 \pm 1.64(\displaystyle\frac{15}{\sqrt{n}} ) = (98,102)\\\\1.64(\frac{15}{\sqrt{n}} ) = 2\\\\n = 151.29 \approx 151[/tex]
Thus, the sample size should be approximately 151.