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
