Question

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 1

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.

Explanation:

1 ) 68% of the data lies within 1 standard deviation of mean

This means 68% of data lies between:
`\mu-\sigma`to
`\mu+\sigma`

2) 95% of the data lies within 2 standard deviation of mean

This means 95% of data lies between:
`\mu-2\sigma`to
`\mu+2\sigma`

3) 99.7% of the data lies within 3 standard deviation of mean

This means 99.7% of data lies between:
`\mu-3\sigma` to
`\mu+3\sigma`

Now,

95% of the data lies within 2 standard deviation of mean :

For Mean =
`\mu = 25`

Standard deviation =
`\sigma = 2`

So, 95% of data lies between:
`25-2(2)`to
`25+2(2)`

95% of data lies between:
`21`to
`29`

For Mean =
`\mu = 25`

Standard deviation =
`\sigma = 3`

So, 95% of data lies between:
`25-2(3)`to
`25+2(3)`

95% of data lies between:
`19`to
`31`

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.