A manufacturer considers his production process to be out of control when defects exceed 3.2%. In a random sample of 136 items,
1 answer:
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Answer:
Is a very improbable event.
Step-by-step explanation:
We want to calculate the probability that the total weight exceeds the limit when the average weight x exceeds 6000/100=60.
If we analyze the situation we this:
If represent the 100 random beggage weights for the n=100 passengers . We assume that for each
for each
the distribution assumed is normal with the following parameters
.
Another important assumption is that the each one of the random variables are independent.
1) First way to solve the problem
The random variable S who represent the sum of the 100 weight is given by:
The mean for this random variable is given by:
And the variance is given by:
And the deviation:
So we have this distribution for S
On this case we are working with the total so we can find the probability on this way:
2) Second way to solve the problem
We know that the sample mean have the following distribution:
If we are interested on the probability that the population mean would be higher than 60 we can find this probability like this:
And with both methods we got the same probability. So it's very improbable that the limit would be exceeded for this case.