Answer :
Answer:
[tex] X \sim N(\mu= 70, \sigma=15)[/tex]
From this info and using the empirical rule we know that we will have about 68% of the scores between:
[tex] \mu -\sigma = 70-15=55[/tex]
[tex] \mu +\sigma = 70+15=85[/tex]
95 % of the scores between:
[tex] \mu -2\sigma = 70-2*15=40[/tex]
[tex] \mu +2\sigma = 70+2*15=100[/tex]
And 99.7% of the values between
[tex] \mu -3\sigma = 70-3*15=25[/tex]
[tex] \mu +3\sigma = 70+3*15=115[/tex]
Step-by-step explanation:
For this problem we can define the random variable of interest as "the student grades" and we know that the distribution for X is given by:
[tex] X \sim N(\mu= 70, \sigma=15)[/tex]
From this info and using the empirical rule we know that we will have about 68% of the scores between:
[tex] \mu -\sigma = 70-15=55[/tex]
[tex] \mu +\sigma = 70+15=85[/tex]
95 % of the scores between:
[tex] \mu -2\sigma = 70-2*15=40[/tex]
[tex] \mu +2\sigma = 70+2*15=100[/tex]
And 99.7% of the values between
[tex] \mu -3\sigma = 70-3*15=25[/tex]
[tex] \mu +3\sigma = 70+3*15=115[/tex]