Answer:
The standard deviation for the mean weigth of Salmon is 2/3 lbs for restaurants, 2/7 lbs for grocery stores and 1/4 lbs for discount order stores.
Step-by-step explanation:
The mean sample of the sum of n random variables is
If 
are indentically distributed and independent, like in the situation of the problem, then the variance of 
will be the sum of the variances, in other words, it will be n times the variance of 
.
However if we multiply this mean by 1/n (in other words, divide by n), then we have to divide the variance by 1/n², thus 
and as a result, the standard deviation of 
is the standard deviation of divided by 
.
Since the standard deviation of the weigth of a Salmon is 2 lbs, then the standard deviations for the mean weigth will be:
- Restaurants: We have boxes with 9 salmon each, so it will be
- Grocery stores: Each carton has 49 salmon, thus the standard deviation is
- Discount outlet stores: Each pallet has 64 salmon, as a result, the standard deviation is
We conclude that de standard deivation of the mean weigth of salmon of the types of shipment given is: 2/3 lbs for restaurants, 2/7 lbs for grocery stores and 1/4 lbs for discount outlet stores.
Answer:
1296√3 cubic units
Step-by-step explanation:
The volume of the prism will be the product of its base area and its height. Since it circumscribes a sphere with diameter 12, that is the height of the prism.
The central cross section of the sphere is a circle of radius 6, and that will be the size of the incircle of the base. That is, the base will have an altitude of 3 times that incircle radius, and an edge length of 2√3 times that incircle radius. Hence the area of the triangular base is ...
B = (1/2)(6×2√3)(6×3) = 108√3 . . . . . square units
The volume of the prism is then ...
V = Bh = (108√3)(12) = 1296√3 . . . cubic units
_____
<em>Comment on the geometry</em>
The centroid of an equilateral triangle is also the incenter and the circumcenter. The distance of that center from any edge of the triangle is 1/3 the height of the triangle. So, for an inradius of 6, the triangle height is 3×6 = 18. The side length of an equilateral triangle is 2/√3 times the altitude, so is 12√3 units for this triangle.
Answer:
a regular trapezium
Step-by-step explanation:
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