In a random sample of 81 audited estate tax​ returns, it was determined that the mean amount of additional tax owed was ​$3408 with a standard deviation of ​$2565. Construct and interpret a​ 90% confidence interval for the mean additional amount of tax owed for estate tax returns. The lower bound is ​$ nothing. ​(Round to the nearest cent as​ needed.) The upper bound is ​$ nothing. ​(Round to the nearest cent as​ needed.) Interpret a​ 90% confidence interval for the mean additional amount of tax owed for estate tax returns. Choose the correct answer below. a. One can be​ 90% confident that the mean additional tax owed is less than the lower boundb. One can be​ 90% confident that the mean additional tax owed is between the lower and upper boundsc. One can be​ 90% confident that the mean additional tax owed is greater than the upper bound.

Answer:B. One can be​ 90% confident that the mean additional tax owed is between the lower and upper bounds.Step-by-step explanation:Given:n= 81[tex]\bar{x}=3408[/tex][tex]\sigma= 2565[/tex]Solution:A confidence interval, in statistics, refers to the probability that a population parameter will fall between two set values for a certain proportion of times. Confidence intervals measure the degree of uncertainty or certainty in a sampling method. A confidence interval can take any number of probabilities, with the most common being a 95% or 99% confidence level.Confidence interval = [tex]\bar{x} \pm z * \frac{\sigma}{\sqrt{n}}[/tex]To Find the z  value:Degree of freedom = n-1 =>81- 1 => 80Significance level = 1- confidence level=>[tex]\frac{(1-\frac{90}{100})}{2}[/tex]=>[tex]\frac{(1-0.90)}{2}[/tex]=> [tex]\frac{0.1}{2}[/tex]=>0.05using this value In T- Distribution table we getz =  1.645Substituting the values  we have,confidence interval = [tex]3408\pm 1.645 * \frac{2565}{\sqrt{81}}[/tex]confidence interval = [tex]3408\pm 1.645 * \frac{2565}{\sqrt{9}}[/tex]confidence interval = [tex]3408\pm 1.645 * 285[/tex]confidence interval = [tex]3408\pm 468.825[/tex]confidence interval= (2939.18, 3876.83)