Question

The scores of eighth-grade students in a math test are normally distributed with a mean of 57.5 and a standard deviation of 6.5. From this data, we can conclude that 68% of the students received scores between and . NextReset

Answer 1

Answer:

$44.5,70.5$

Step-by-step explanation:

Empirical Rule-

1. 68% of data falls within the one standard deviation from the mean.
2. 95% fall within two standard deviations from the mean.
3. 99.7% fall within three standard deviations from the mean.

Here, the normal distribution has the mean as 57.5 and standard deviation as 6.5

So the 68% of the score will lie between,

$=\mu \pm 2\sigma$

$=57.5\pm 2(6.5)$

$=57.5\pm 13$

$=44.5,70.5$

Answer 2

Approximately 68% of a normal distribution lies within one standard deviation of the mean, so this corresponds to students with scores between $(57.5-6.5,57.5+6.5)=(51,64)$.