A supplier makes packaging cartons for a customer, with a length normally distributed around a mean of 150mm. Due to the cavity
1 answer:
Answer:
a) Cp=0.93
b) The probability of having non-conforming items is P=0.0051.
As percentage is 0.51%.
Step-by-step explanation:
a) The Cp is a measure of the capability of the process to produce items within the specifications.
It can be expressed as:
Where USL: upper specification limits
LCL: lower specification limits
b) The upper and lower specifications are equally distant from the mean (±7mm), so we can calculate z as:
The probability of having non-conforming items is P=0.0051.
As percentage is 0.51%.
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Answer:
The upper 20% of the weighs are weights of at least X, which is , in which
is the standard deviation of all weights and
is the mean.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Upper 20% of weights:
The upper 20% of the weighs are weighs of at least X, which is found when Z has a p-value of 0.8. So X when Z = 0.84. Then
The upper 20% of the weighs are weights of at least X, which is , in which
is the standard deviation of all weights and
is the mean.