Question

The town of KnowWearSpatial, U.S.A. operates a rubbish waste disposal facility that is overloaded if its 5030 households discard waste with weights having a mean that exceeds 26.49 lb/wk. For many different weeks, it is found that the samples of 5030 households have weights that are normally distributed with a mean of 26.23 lb and a standard deviation of 12.49 lb.

What is the proportion of weeks in which the waste disposal facility is overloaded?
P(M > 26.49) =
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

Answer:

Given,

Mean = 26.23

Standard deviation = 12.49

n = 5030

x = /sqrt(n)

substitute values

= 12.49/sqrt(5030)

= 0.1761

P(M > 26.49) = P((M-m)/m > (26.49 - 26.23)/0.1761)

= P(z > 1.4764)

= 0.0699183 [since from z table]

= 0.0699

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