Question

The town of KnowWearSpatial, U.S.A. operates a rubbish waste disposal facility that is overloaded if its 4755 households discard waste with weights having a mean that exceeds 27.35 lb/wk. For many different weeks, it is found that the samples of 4755 households have weights that are normally distributed with a mean of 26.98 lb and a standard deviation of 12.64 lb.

What is the proportion of weeks in which the waste disposal facility is overloaded?
P(M > 27.35) =
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?

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

Answer 1

Solution :

= / n = 12.64 / 4755

P(M > 27.35) = 1 - P( < 27.35)

= 1 - P[( - ) / < (27.35 - 26.98) / 12.64 / 4755]

= 1 - P(z < 2.018)

= 0.0218

Yes, this is an acceptable level because it is unusual for the system to be overloaded.​​​​​​​