oxes of cereal produced in a given factory are regularly inspected and must contain an average weight of 500 grams. The individual box weights are assumed to follow a normal distribution with a mean of 500 and a standard deviation of 20 grams. In routine inspections, the inspector selects a random sample of 14 cereal boxes and if the average sample weight is below 495 or above 505, the manufacturing process is stopped and the box filling machine is adjusted. Boxes of cereal produced in a given factory are regularly inspected and must contain an average weight of 500 grams. The individual box weights are assumed to follow a normal distribution with a mean of 500 and a standard deviation of 20 grams. In routine inspections, the inspector selects a random sample of 14 cereal boxes and if the average sample weight is below 495 or above 505, the manufacturing process is stopped and the box filling machine is adjusted. a. Do you want to know what is the mean sample weight that is exceeded by 5% of the samples? b. Considering the machine adjusted, what is the probability of finding an average sample weight outside the limits [495, 505]? c. Considering the machine adjusted, what should be the critical value Δ (in grams) such that P(μ−Δ ≤Y¯ ≤μ+Δ)=0.95?
Boxes of cereal produced in a given factory are regularly inspected and must contain an average weight of 500 grams. The individual box weights are assumed to follow a
Boxes of cereal produced in a given factory are regularly inspected and must contain an average weight of 500 grams. The individual box weights are assumed to follow a normal distribution with a mean of 500 and a standard deviation of 20 grams. In routine inspections, the inspector selects a random sample of 14 cereal boxes and if the average sample weight is below 495 or above 505, the manufacturing process is stopped and the box filling machine is adjusted.
a. Do you want to know what is the mean sample weight that is exceeded by 5% of the samples?
b. Considering the machine adjusted, what is the
c. Considering the machine adjusted, what should be the critical value Δ
(in grams) such that P(μ−Δ ≤Y¯ ≤μ+Δ)=0.95?
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