Determine the minimum sample size required when you want to be 99​% confident that the sample mean is within one unit of the population mean and sigmaequals15.2. Assume the population is normally distributed.

Answer: 1534Step-by-step explanation:The formula used to find the sample size :-[tex]n=(\dfrac{z_{\alpha/2}\cdot\sigma}{E})^2[/tex] , where [tex]\sigma=[/tex] Population standard deviation.E= Margin of error [tex]z_{\alpha/2}[/tex]= Two-tailed z-value for significance level of [tex]\alpha[/tex].Given : Confidence level : 99%Then significance level : [tex]\alpha=1-0.99=0.01[/tex]Two-tailed z-value: [tex]z_{\alpha/2}=z_{0.005}=2.576[/tex]  [using z-value table] [tex]\sigma= 15.2[/tex] Margin of error : 1 unit.We assume the population is normally distributed.Then, the required minimum sample size :-[tex]n=(\dfrac{(2.576)\cdot15.2}{1})^2[/tex] Simplify ,[tex]n=1533.12968704\approx1534[/tex]∴ Required minimum sample size = 1534