Answer:
As both the mean and standard deviation are in the desired ranges, the tool passes the technical control.
Step-by-step explanation:
Mean of the batch:
The mean of the batch is the sum of all values divided by the number of items. So
[tex]M = \frac{199+204+201+197+195+204+200}{7} = 200[/tex]
Mean in the desired interval.
Standard deviation:
Square root of the sum of the difference squared between each term and the mean, divided by the number of items. So
[tex]S = \sqrt{\frac{(199-200)^2+(204-200)^2+(201-200)^2+(197-200)^2+(195-200)^2+(204-200)^2+(200-200)^2}{7}} = 1.18[/tex]
As both the mean and standard deviation are in the desired ranges, the tool passes the technical control.
