Answer:
The standard deviation is above 6 mm, which means that this batch does not pass 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{31+32+38+34+45+41+24}{7} = 35[/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 itens. So
[tex]S = \sqrt{\frac{(31-35)^2+(32-35)^2+(38-35)^2+(34-35)^2+(45-35)^2+(41-35)^2+(24-35)^2}{7}} = 6.46[/tex]
The standard deviation is above 6 mm, which means that this batch does not pass the technical control.
