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The distribution of actual weights of 8-ounce chocolate bars produced by a certain machine is Normal, with a mean of 8.1 ounces and a standard deviation of 0.1 ounces. What weight should be put on the chocolate bar wrappers so that only 1% of bars are underweight?

Respuesta :

Answer:

We are given:

[tex]\mu=8.1, \sigma=0.1[/tex]

We have to first find the z value corresponding to area 0.01. Using the standard normal table, we have:

[tex]z_{0.01}=-2.33[/tex]

Now using the z-score formula, we have:

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

[tex]-2.33=\frac{x-8.1}{0.1}[/tex]

[tex]-0.233=x-8.1[/tex]

[tex]x=8.1-0.233[/tex]

[tex]x=7.867[/tex] ounces.

Therefore, the weight that should be put on the chocolate bar wrappers so that only 1% of bars are underweight is 7.867 ounces.

 

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