The labels on boxes of Cheesy Poofs say that the box contains 16 ounces of Cheesy Poofs, but that doesn’t guarantee that each box contains exactly 16.00 ounces. The machine that fills the boxes doesn’t always put out the exact same amount. The amount in each box is Normally distributed, and has a standard deviation is .40 ounces. To help assure that most boxes contain as much or more than the label says, the machine is set so that the mean will be 16.28 ounces. What proportion of the boxes contain…                                           a)   …less than 16.00 ounces?b)   …between 16.00 and 17.00 ounces?c)…more than 16.50 ounces?

Question
Asked Oct 1, 2019
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The labels on boxes of Cheesy Poofs say that the box contains 16 ounces of Cheesy Poofs, but that doesn’t guarantee that each box contains exactly 16.00 ounces. The machine that fills the boxes doesn’t always put out the exact same amount. The amount in each box is Normally distributed, and has a standard deviation is .40 ounces. To help assure that most boxes contain as much or more than the label says, the machine is set so that the mean will be 16.28 ounces. What proportion of the boxes contain…                                           

a)   …less than 16.00 ounces?

b)   …between 16.00 and 17.00 ounces?

c)…more than 16.50 ounces?

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Expert Answer

Step 1

It is given that mean and standard deviation are of 16.28 and 0.40, respectively.

Step 2

a)

The proportion of the boxes contain less than 16.00 ounces is obtained as follows:

х — и
16.00 16.28
Z =
0.40
Z 0.70
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Image Transcriptionclose

х — и 16.00 16.28 Z = 0.40 Z 0.70

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Step 3

The proportion of the boxes contain less than 16.00 ounces represents the area to the left of –0.70.

The area to the left of –0.70 using standard normal table is 0.2420. Therefore, proportion of the boxes contain less than 16.00 ounces is 0.2420.

b)

The proportion of the boxes contain between 16.00 ounces is 17.00 ounces is obtained as follows:

The...

17.00-16.28
Z =
0.40
Z 1.80
help_outline

Image Transcriptionclose

17.00-16.28 Z = 0.40 Z 1.80

fullscreen

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