Question

Suppose the scores on a test given to all juniors in a school district are normally distributed with a mean of 74 and a standard deviation of 8. On a separate sheet of paper, draw a Normal Curve and label the mean, standard deviations, and the associated percentages.

Answer 1

`\mu -\sigma = 66 , \mu +\sigma = 82`

`\mu -2\sigma = 58 , \mu +2\sigma = 90`

`\mu -3\sigma = 50 , \mu +3\sigma = 98`

And in the figure attached we see the limits with the percentages associated.

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:

`X \sim N(\mu= 74, \sigma =8)`

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:

`\mu -\sigma = 66 , \mu +\sigma = 82`

`\mu -2\sigma = 58 , \mu +2\sigma = 90`

`\mu -3\sigma = 50 , \mu +3\sigma = 98`

And in the figure attached we see the limits with the percentages associated.