Question

Math , pleaaaase

You are given the results of measurements of sizes of a crushed stone for road
construction. The technical requirement is the following: The mean size of the stones must be in the interval [33-36] mm and standard deviation must be smaller than 6 mm. Will this batch pass the technical control?

Answer 1

The standard deviation is above 6 mm, which means that this batch does not pass the technical control.

Explanation:

Mean of the batch:

The mean of the batch is the sum of all values divided by the number of items. So

`M = (31+32+38+34+45+41+24)/(7) = 35`

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

`S = \sqrt{((31-35)^2+(32-35)^2+(38-35)^2+(34-35)^2+(45-35)^2+(41-35)^2+(24-35)^2)/(7)} = 6.46`

The standard deviation is above 6 mm, which means that this batch does not pass the technical control.