Question

Suppose the scores of students on an homework are normally distributed with a mean of 318...

Suppose the scores of students on an homework are normally distributed with a mean of 318 and a standard deviation of 40. According to the empirical rule, what percentage of students scored between 238 and 398 on the homework?

Answer:  %

Math   Statistics-And-Probability   
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Answer #1

Given:

Mean, = 318

Standard deviation, = 40

According to Empirical rule (three sigma rule) 68%, 95% and 99.7% lies within 1, 2 and 3 standard deviations of mean.

So

68% data values lies within One standard deviation of the mean

95% data values lies within Two standard deviation of the mean

99.7% data values lies within Three standard deviation of the mean

Now,

The percentage of students scored between 238 and 398 on the homework :

238 is 2 standard deviations below mean

398 is 2 standard deviations above mean

Using empirical rule, 95% percentage of students scored between 238 and 398 on the homework.

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