Question

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.?

Answer 1

Answer: 0.0668

Step-by-step explanation:

As per given description, we have

$\mu=90\ lbs\ \ \ ;\ \sigma=24\ lbs$

n= 36

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

z-score : $\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

For x= 84 lb , we have

$\dfrac{84-90}{\dfrac{24}{\sqrt{36}}}=-1.5$

P-value : $P(x$

$\\=1-0.9331927=0.0668072\approx0.0668$

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