Answer:
[tex] \mu -\sigma = 66 , \mu +\sigma = 82[/tex]
[tex] \mu -2\sigma = 58 , \mu +2\sigma = 90[/tex]
[tex] \mu -3\sigma = 50 , \mu +3\sigma = 98[/tex]
And in the figure attached we see the limits with the percentages associated.
Step-by-step explanation:
For this case we know that the random variable of interest is the scores on a test given to all juniors in a school district follows a normal distribution with the following parameters:
[tex] X \sim N(\mu= 74, \sigma =8)[/tex]
For this case we know from the empirical rule that within one deviation from the mean we have approximately 68.2% of the data, within 2 deviations from the mean we have 95% and within 3 deviation 99.7%
We can find the limits and we got:
[tex] \mu -\sigma = 66 , \mu +\sigma = 82[/tex]
[tex] \mu -2\sigma = 58 , \mu +2\sigma = 90[/tex]
[tex] \mu -3\sigma = 50 , \mu +3\sigma = 98[/tex]
And in the figure attached we see the limits with the percentages associated.
