The test scores for a very large statistics class have a mound-shaped distributi

Question

The test scores for a very large statistics class have a mound-shaped distribution with a mean of 70%. a.) If 16% of all students in the class scores above 85, what is the standard deviation of the scores? b.) If 95% of the scores are between 60 and 80, what is he standard deviation? The test scores for a very large statistics class have a mound-shaped distribution with a mean of 70%. a.) If 16% of all students in the class scores above 85, what is the standard deviation of the scores? b.) If 95% of the scores are between 60 and 80, what is he standard deviation? a.) If 16% of all students in the class scores above 85, what is the standard deviation of the scores? b.) If 95% of the scores are between 60 and 80, what is he standard deviation?

Explanation / Answer

a)Since the distribution is moud shaped it can be assumed to be normal.

Now it is known that 68% of the data of a normal distribution lie within 1 standard deviation from the mean. So, 32% of the data lie outside and 16% of data lie in each tail. If 16% of all students is above 85, then 85 is one standard deviation from mean 70% and the standard deviation is 85-70=15

b)Similarly 95% of the data lie within 2 standard deviations from the mean. Now 95% data falls within 60 and 80.

So, mean+2 sd=80

and mean-2 sd=60

that is 70+2*sd=80

or sd=(80-70)/2=5

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