Question

The distribution of scores on a test is​ mound-shaped and symmetric with a mean score of 78. If​ 68% of the scores fall between 72 and​ 84, which is most likely to be the standard deviation of the​ distribution?

Answer 1

Answer:

The standard deviation for the distribution of scores is 6.    

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 78

We are given that the distribution of score is a bell shaped distribution that is a normal distribution.

Empirical Formula:

• Almost all the data lies within three standard deviation from mean for a normal data.
• for this rule almost all the data lies within on tandard deviation from the mean.

68% of the scores fall between 72 and​ 84, thus, we can write:

$\mu + \sigma = 84\\\mu - \sigma = 72\\78 - \sigma = 72\\\Rightarrow \sigma = 6$

Thus, the standard deviation for the distribution of scores is 6.