High School

Assume that the cartons of materials being moved to new offices are normally distributed with a mean weight of 80 pounds and a standard deviation of 15 pounds. If a sample of 30 boxes is selected, what is the probability that the sample mean weight is 84 pounds or more? Would a sample mean weight of 84 pounds or more be unusual?

Answer should have one digit before the decimal and at least 4 after (Ex: 0.XXXX).

Probability: ___________

Is it unusual (yes or no)? ___________

Answer :

Answer:

Probability: 0.0721

Unusual: no

Step-by-step explanation:

You want to know if a sample of 30 boxes of a population with mean weight of 80 pounds and standard deviation of 15 pounds having a sample mean weight of 84 pounds or more is unusual.

Probability

The sample mean distribution will have a standard deviation of ...

[tex]s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{15}{\sqrt{30}}\approx2.73861[/tex]

The z-score of the sample mean is ...

[tex]z=\dfrac{x-\mu}{s}=\dfrac{84-80}{2.73861}\approx1.46059[/tex]

The probability a normally-distributed variable will exceed that z-score is ...

[tex]\boxed{P(\mu_s\ge84)\approx0.0721}[/tex]

Unusual

Whether this is "unusual" depends on your definition. Quite often, "unusual" is considered to be something that has a probability less than 5% of occurring "by chance". Depending on what it is and the cost of being "unusual", that probability threshold may be reduced to 1%, or even 0.0001% or less.

By most reasonable definitions, a probability of 0.0721, or 1 chance in 13.9, is not unusual.