Answer :
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:
[tex]\mu + \sigma = 84\\\mu - \sigma = 72\\78 - \sigma = 72\\\Rightarrow \sigma = 6[/tex]
Thus, the standard deviation for the distribution of scores is 6.
The standard deviation for the distribution of scores is 6.
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.
What is the 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 standard deviation from the mean.
68% of the scores fall between 72 and 84, thus, we can write
[tex]\mu +\sigma =84[/tex]
[tex]\mu +\sigma =72\\78 -\sigma =72\\\sigma=6[/tex]
Therefore , the standard deviation for the distribution of scores is 6.
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