9. Which of the following is TRUE? ( 5 points) a. For a data set with mean = 25 pounds and Standard Deviation = 2 pounds then 95% of the data is between 23 pounds and 27 pounds. b. For a data set with mean = 25 pounds and Standard Deviation = 3 pounds then 95% of the data is between 22 pounds and 28 pounds. c. For a data set with mean = 25 pounds and Standard Deviation = 3 pounds then 65% of the data is between 19 pounds and 31 pounds. d. For a data set with mean = 25 pounds and Standard Deviation = 3 pounds then 95% of the data is between 19 pounds and 31 pounds.

Answer:For a data set with mean = 25 pounds and Standard Deviation = 3 pounds then 95% of the data is between 19 pounds and 31 pounds.Step-by-step explanation:1 ) 68% of the data lies within 1 standard deviation of mean   This means 68% of data lies between:[tex]\mu-\sigma[/tex]to [tex]\mu+\sigma[/tex]2) 95% of the data lies within 2 standard deviation of mean  This means 95% of data lies between:[tex]\mu-2\sigma[/tex]to [tex]\mu+2\sigma[/tex]3) 99.7% of the data lies within 3 standard deviation of meanThis means 99.7% of data lies between:[tex]\mu-3\sigma[/tex] to[tex]\mu+3\sigma[/tex]Now,95% of the data lies within 2 standard deviation of mean  :For Mean = [tex]\mu = 25[/tex]Standard deviation = [tex]\sigma = 2[/tex]So,  95% of data lies between:[tex]25-2(2)[/tex]to [tex]25+2(2)[/tex] 95% of data lies between:[tex]21[/tex]to [tex]29[/tex]For Mean = [tex]\mu = 25[/tex]Standard deviation = [tex]\sigma = 3[/tex]So,  95% of data lies between:[tex]25-2(3)[/tex]to [tex]25+2(3)[/tex] 95% of data lies between:[tex]19[/tex]to [tex]31[/tex]So, Option D is true For a data set with mean = 25 pounds and Standard Deviation = 3 pounds then 95% of the data is between 19 pounds and 31 pounds.