Question

COF

Answer 1

Answer:

$X \sim N(\mu= 70, \sigma=15)$

From this info and using the empirical rule we know that we will have about 68% of the scores between:

$\mu -\sigma = 70-15=55$

$\mu +\sigma = 70+15=85$

95 % of the scores between:

$\mu -2\sigma = 70-2*15=40$

$\mu +2\sigma = 70+2*15=100$

And 99.7% of the values between

$\mu -3\sigma = 70-3*15=25$

$\mu +3\sigma = 70+3*15=115$

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:

$X \sim N(\mu= 70, \sigma=15)$

From this info and using the empirical rule we know that we will have about 68% of the scores between:

$\mu -\sigma = 70-15=55$

$\mu +\sigma = 70+15=85$

95 % of the scores between:

$\mu -2\sigma = 70-2*15=40$

$\mu +2\sigma = 70+2*15=100$

And 99.7% of the values between

$\mu -3\sigma = 70-3*15=25$

$\mu +3\sigma = 70+3*15=115$