The best estimate of the standard deviation of the population is 75
The given parameter is:
Sample size, n
The estimate of the standard deviation of the population is calculated using:
[tex]\sigma_x = \frac{\sigma}{\sqrt n}[/tex]
This gives
[tex]\sigma_x = \frac{\sigma}{\sqrt 25}[/tex]
Evaluate the square root
[tex]\sigma_x = \frac{\sigma}{5}[/tex]
Multiply both sids by 5
[tex]\sigma = 5\sigma_x[/tex]
From the normal curve, we have:
[tex]\sigma_x = 15[/tex] -- the difference between the scores
So,we have:
[tex]\sigma = 5 * 15[/tex]
[tex]\sigma = 75[/tex]
Hence, the estimate of the standard deviation of the population is 75
Read more about standard deviation at:
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