The town of KnowWearSpatial, U.S.A. operates a rubbish waste disposal facility that is overloaded if its 4699 households discard waste with weights having a mean that exceeds 26.94 lb/wk. For many different weeks, it is found that the samples of 4699 households have weights that are normally distributed with a mean of 26.53 lb and a standard deviation of 12.87 lb.
What is the proportion of weeks in which the waste disposal
facility is overloaded?
P(M > 26.94) =
Enter your answer as a number accurate to 4 decimal places. NOTE:
Answers obtained using exact z-scores or z-scores
rounded to 3 decimal places are accepted.
Is this an acceptable level, or should action be taken to correct a
problem of an overloaded system?
Given that, mean = 26.53
lb
standard deviation = 12.87
lb
sample size ( n ) = 4699
We want to find, P(M > 26.94)
=> P(M > 26.94) = 0.0145
Since, 0.0145 < 0.05, it is unusual.
Yes, this is an acceptable level because it is unusual for the system to be overloaded.
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