A manufacturing company measures the weight of boxes before shipping them to the customers. If the box weights have a population mean and standard deviation of 90 lbs. and 24 lbs., respectively, then based on a sample size of 36 boxes, what is the probability that the average weight of the boxes will be less than 84 lbs.?

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JeanaShupp JeanaShupp · Answer 1 · 2019-10-23T05:57:03+02:00

Answer: 0.0668

Step-by-step explanation:

As per given description, we have

[tex]\mu=90\ lbs\ \ \ ;\ \sigma=24\ lbs[/tex]

n= 36

Let x be a random variable that represents the weight of boxes.

z-score : [tex]\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

For x= 84 lb , we have

[tex]\dfrac{84-90}{\dfrac{24}{\sqrt{36}}}=-1.5[/tex]

P-value : [tex]P(x<84)=P(z<-1.5)=1-P(z<1.5)[/tex]

[tex]\\=1-0.9331927=0.0668072\approx0.0668[/tex]

Hence, the probability that the average weight of the boxes will be less than 84 lbs. = 0.0668