Consumer products are required by law to contain at least as much as the amount printed on the package. For example, a bag of potato chips that is labeled as 10 ounces should contain at least 10 ounces.Assume that the standard deviation of the packaging equipment yields a bag weight standard deviation of 0.2 ounces. Assume the bag weight distribution is bell-shaped. Determine what average bag weight must be used to achieve at least 99 percent of the bags having 10 or more ounces in the bag.

Question

contestada

Respuesta :

lublana lublana · Answer 1 · 2021-07-16T07:15:49+02:00

Answer:

The average bag weight must be used to achieve at least 99 percent of the bags having 10 or more ounces in the bag=9.802

Step-by-step explanation:

We are given that

Standard deviation, [tex]\sigma=0.2[/tex]ounces

We have to find the average bag weight must be used to achieve at least 99 percent of the bags having 10 or more ounces in the bag.

[tex]P(x\geq 10)=0.99[/tex]

Assume the bag weight distribution is bell-shaped

Therefore,

[tex]P(\frac{x-\mu}{\sigma}\geq 10)=0.99[/tex]

We know that

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Using the value of z

Now,

[tex]\frac{10-\mu}{0.2}=0.99[/tex]

[tex]10-\mu=0.99\times 0.2[/tex]

[tex]\mu=10-0.99\times 0.2[/tex]

[tex]\mu=9.802[/tex]

Hence, the average bag weight must be used to achieve at least 99 percent of the bags having 10 or more ounces in the bag=9.802