Many medical professionals believe that eating too much red meat increases the risk of heart disease and cancer (WebMD website, March 12, 2014). Suppose you would like to conduct a survey to determine the yearly consumption of beef by a typical American and want to use 3 pounds as the desired margin of error for a 99% confidence interval of the population mean amount of beef consumed annually. Use 25 pounds as a planning value for the population standard deviation. How large a sample should be taken?

Answer: 461Step-by-step explanation:Formula to find the sample size is given by :-[tex]n=(\dfrac{z_{\alpha/2}\cdot \sigma}{E})^2[/tex]Given : Margin of error : E=  3 pounds Standard deviation: [tex]\sigma= 25\ pounds[/tex]Critical value for 99% confidence interval (Two-tailed ): [tex]z_{\alpha/2}=2.576[/tex]Required sample size = [tex]n=(\dfrac{(2.576)\cdot 25}{3})^2[/tex][tex]=460.817777778\approx461[/tex]Hence, the required sample size = 461