Question

The town of KnowWearSpatial, U.S.A. operates a rubbish waste disposal facility that is overloaded if its 5055 households discard waste with weights having a mean that exceeds 26.96 lb/wk. For many different weeks, it is found that the samples of 5055 households have weights that are normally distributed with a mean of 26.64 lb and a standard deviation of 12.56 lb.

What is the proportion of weeks in which the waste disposal facility is overloaded?
P(M > 26.96) =
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?

• No, this is not an acceptable level because it is not unusual for the system to be overloaded.
• Yes, this is an acceptable level because it is unusual for the system to be overloaded.

Answer 1

Solution :

Given that,

mean = = 26.64 lb

standard deviation = = 12.56 lb

n = 5055

= = 26.64 lb

= / n = 12.56 / 5055 = 0.1767

P(M > 26.96) = 1 - P(M < 26.96)

= 1 - P[(M - ) / < (26.96 - 26.64) / 0.1767 ]

= 1 - P(z < 1.811)

Using z table,    

= 1 - 0.9649

= 0.0351

Yes, this is an acceptable level because it is unusual for the system to be overloaded. because probability is less than 0.05