Question

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…                           

Complete the following sentences.

7. Half of the boxes of Cheesy Poofs produced which are labeled 16 ounces, actually contain more than

____________________ounces.

8. 14% of the boxes of Cheesy Poofs produced which are labeled 16 ounces, actually contain more than

____________________ounces.

Answer 1

Solution:

Given: The amount in each box is Normally distributed with the mean of 16.28 ounces and a standard deviation of 0.40 ounces.

That is:

Part g) Half of the boxes of Cheesy Poofs produced which are labeled 16 ounces, actually contain more than ___ounces?

That is find x value such that:

P( X > x ) = 50%

P( X > x ) = 0.5000

Thus find z value such that:

P( Z > z ) = 0.5000

that is find z value such that:

P( Z < z ) = 1 - P( Z > z)

P( Z < z ) = 1 - 0.5000

P( Z < z ) = 0.5000

Look in z table for area = 0.5000 or its closest area and find z value.

Area 0.5000 corresponds to 0.0 and 0.00

Thus z = 0.00

Use following formula to find x value:

Thus Half of the boxes of Cheesy Poofs produced which are labeled 16 ounces, actually contain more than 16.28 ounces.

Part h) 14% of the boxes of Cheesy Poofs produced which are labeled 16 ounces, actually contain more than ___ounces.

That is find:

P( X > x ) = 14%

P( X > x ) = 0.1400

Thus find z value such that:

P( Z > z ) = 0.1400

that is find z value such that:

P( Z < z ) = 1 - P( Z > z)

P( Z < z ) = 1 - 0.1400

P( Z < z ) = 0.8600

Look in z table for area = 0.8600 or its closest area and find z value.

Area 0.8599 is closest to 0.8600 and it corresponds to 1.0 and 0.08

thus z= 1.08

Use following formula to find x value:

Thus 14% of the boxes of Cheesy Poofs produced which are labeled 16 ounces, actually contain more than 16.712 ounces.