Answer: Option (A) The new standard deviation is greater than $27.
Explanation:
If a sixth skateboard having price of $450 is added to the sample, the new sample set will be the following:
75, 82, 100, 120, 140, 450.
Let us first find the mean of the above sample set.
Mean = [tex]\overline{x}=\frac{75+82+100+120+140+450}{6}\\ \overline{x} \approx 161.167[/tex]
Now that we have mean, let's find the variance.
[tex]s^2 = \frac{\underset{i} \sum (x_i - \overline x)^2}{n-1}[/tex]
Where n is the number of samples in the set (which in this case is 6).
[tex]s^2 = \frac{(75-161.167)^2+(82-161.167)^2+(100-161.167)^2+(120-161.167)^2+(140-161.167)^2+(450-161.167)^2}{6-1} \\s^2 = 20600.167[/tex]
Now that we have variance, it's time to find the new standard deviation by taking the square-root of the variance, as follows:
[tex]\sqrt{s^2} = \sqrt{20600.167} \\s \approx 143.53[/tex]
$143.53 > $27
New standard deviation is greater than the old standard deviation.
Therefore, the correct answer is Option (A) The new standard deviation is greater than $27.
