Question

Exercise 11.0:The mean weight of boxes shipped by a company is 12 lbs, with a standard deviation of 4 lbs. Assume weight of boxes follows Normal Distribution. Boxes are shipped in palettes of 10 boxes. The shipper has a limit of 150 lbs for such shipments. What’s the probability that a palette of 10 boxes will exceed that limit (150 lbs)? HINT: Prob (total weight of a sample of 10 boxes >150 lbs) = Prob (the sample mean weight ( ) > 15 lbs)푦

Answer 1

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, $\mu_{\bar x}=\mu$ and standard deviation, $\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}$.

Compute the probability that the sample mean weight of the 10 boxes exceed 15 lbs as follows:

$P(\bar X>15)=P(\frac{\bar X-\mu_{\bar x}}{\sigma/\sqrt{n}}>\frac{15-12}{4/\sqrt{10}})\\=P(Z>2.37)\\=1-P(Z$

*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.