A machine fills boxes with cereal. The boxes are labeled as containing 24 ounces but there is some variability; the amount deposited into the box is normally distributed with a standard deviation of 0.25 ounce. What does the mean have to be in order for 99% of the boxes to contain 24 ounces or more of cereal?

The mean amount of cereal in a box must be 23.42 ounces.

Step-by-step explanation:

Let X = amount of cereal in a box.

It is provided that X follows a normal distribution with mean μ and standard deviation σ = 0.25.

If 99% of the boxes contain 24 ounces or more of cereals then the probability statement is:

Use the z table to determine the z-value.

The value of z is -2.33.

Determine the value of μ as follows:

Thus, the mean amount of cereal in a box must be 23.42 ounces.

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step-by-step explanation: