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

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:$\mu-\sigma$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.