Answer in Statistics and Probability for anand #87118

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

“z_{alpha/2}=z_{0.025}=1.96”

We have that

“bar{X}=60, sigma^2=25, n=16”

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

“57.55lemule62.45”

Hence

“95 % CI [57.55, 62.45]”