Respuesta :
Answer:
The probability that a palette of 10 boxes will exceed the limit of 150 lbs is 0.0089.
Step-by-step explanation:
Let X = the weight of boxes shipped by a company.
The random variable x follows a Normal distribution with mean, μ = 12 lbs and standard deviation, σ = 4 lbs.
Each palettes shipped, contains n = 10 boxes.
The sample mean weight of the boxes follows a Normal distribution with mean, [tex]\mu_{\bar x}=\mu[/tex] and standard deviation, [tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex].
Compute the probability that the sample mean weight of the 10 boxes exceed 15 lbs as follows:
[tex]P(\bar X>15)=P(\frac{\bar X-\mu_{\bar x}}{\sigma/\sqrt{n}}>\frac{15-12}{4/\sqrt{10}})\\=P(Z>2.37)\\=1-P(Z<2.37)\\=1-0.9911\\=0.0089[/tex]
*Use a z-table for the probability.
Thus, the probability that a palette of 10 boxes will exceed the limit of 150 lbs is 0.0089.
