Answer in Statistics and Probability for Anand #86838

For a single mean from a normal distribution with known variance, a two-sided, 100(1 – α)% confidence interval is calculated by

“bar{X}-z_{alpha/2}*{sigma over sqrt{n}}lemulebar{X}+z_{alpha/2}*{sigma over sqrt{n}}”

For a 95% confidence interval for μ

“z_{alpha/2}=z_{0.025}=1.96”

We have that

“bar{X}=60, sigma^2=25, n”

Then

“60-1.96*{sqrt{25} over sqrt{n}}lemule60+1.96*{sqrt{25} over sqrt{n}}”

“60-{9.8 over sqrt{n}}lemule60+{9.8 over sqrt{n}}”

“95% CI [60-{9.8 over sqrt{n}}, 60+{9.8 over sqrt{n}}]”

If n=16

“60-1.96*{sqrt{25} over sqrt{16}}lemule60+1.96*{sqrt{25} over sqrt{16}}”

“57.55lemule62.45”

“95% CI [57.55, 62.45]”