question archive The manager of a cold beverage plant is redesigning assembly line of filling bottles labeled as 1000 ml
The manager of a cold beverage plant is redesigning assembly line of filling bottles labeled as 1000 ml
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The manager of a cold beverage plant is redesigning assembly line of filling bottles labeled as 1000 ml. According to government regulations, not more than 0.5% of the bottles should contain less amount of beverage than what is displayed on the label. For cost reasons, the manager wants to maintain the average amount of beverage filled at 1010 ml. Assume that the volume of beverage in the bottles is normally distributed. What standard deviation should the manager target so that the plant meets the regulatory requirement?
Select one:
A. 3.88
B. 2.58
C. -2.58
D. -3.88
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Answer: Option A. 3.88 ml
Step-by-step explanation
Government regulation says that the allowable bottles containing less than 1000 ml must only be 0.5%.
Since X = 1000 ml, and according to the manager the mean = 1010 ml, standard deviation must be = ?.
0.5%/100 = 0.005, that is P(z=?) = 0.005,
So looking at your table for the value of z-score for probability/area of 0.005;
z = -2.58.
Now to find the standard deviation, use the z-score formula:
- z = (X-mean)/sd
- -2.58 = (1000-1010)/sd
- sd = (1000-1010)/-2.58
- sd = 3.876 or 3.88 ml.
