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.

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wifilethbridge wifilethbridge · Answer 1 · 2019-09-26T08:56:04+02:00

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 mean

This 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.