On a final examination in Biology, the mean

christina nose

christina nose

Answered question

2022-06-15

On a final examination in Biology, the mean mark was 72 and the standard deviation was 15.Determine the standard variable of students receiving marks 60 and 92.

Answer & Explanation

nick1337

nick1337

Expert2023-05-21Added 777 answers

To determine the standard variable of students receiving marks 60 and 92 on a final examination in Biology, we can use the formula for standard deviation.
The standard deviation (σ) measures the spread or dispersion of a set of data points. It is calculated as the square root of the variance (σ^2), where the variance is the average of the squared differences from the mean.
Given that the mean mark on the examination is 72 and the standard deviation is 15, we can calculate the standard variable for a specific mark using the following formula:
Z=xμσ,
where Z is the standard variable, x is the specific mark, μ (mu) is the mean mark, and σ (sigma) is the standard deviation.
Let's calculate the standard variable for a mark of 60:
Z1=607215=1215=0.8
Therefore, the standard variable for a mark of 60 is -0.8.
Now, let's calculate the standard variable for a mark of 92:
Z2=927215=2015=1.333
Therefore, the standard variable for a mark of 92 is 1.333.
In summary, the standard variable for a mark of 60 is -0.8, and the standard variable for a mark of 92 is 1.333.

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