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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.
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