Question

a data set is normally distributed and has a mean of 270 with a standard deviation of 17. using the graphic below, rhonda was adamant that her values that were one standard deviation away from the mean were 269 and 271. is she correct?
standard normal distribution
no, she should have subtracted 217 from the mean and added 217 to the mean. her answer should have been 236 and 304.
no, she should have added 17 from the mean. her answer should have been 287
no, she should have subtracted 17 from the mean. her answer should have been 236.
no, she should have subtracted 17 from the mean and added 17 to the mean. her answer should have been 253 and 287

Explanation:

Step1: Recall formula for values one - std dev from mean

Values one standard deviation away from the mean in a normal distribution are $\mu-\sigma$ and $\mu + \sigma$, where $\mu$ is the mean and $\sigma$ is the standard deviation.

Step2: Identify given values

Given $\mu = 270$ and $\sigma=17$.

Step3: Calculate lower value

$\mu-\sigma=270 - 17=253$.

Step4: Calculate upper value

$\mu+\sigma=270 + 17=287$.

Answer:

No, she should have subtracted 17 from the mean and added 17 to the mean. Her answer should have been 253 and 287.