Answer:
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:
[tex]\geq P(X \geq 24) = 0.99\\P(\frac{X-\mu}{\sigma}\geq \frac{24-\mu}{0.25})=0.99\\P(Z \geq z)=0.99\\1-P(Z<z)=0.99\\P(Z<z)=0.01[/tex]
Use the z table to determine the z-value.
The value of z is -2.33.
Determine the value of μ as follows:
[tex]\frac{24-\mu}{0.25}=-2.33 \\\mu=24-(2.33\times 0.25)\\=23.4175\\\approx23.42[/tex]
Thus, the mean amount of cereal in a box must be 23.42 ounces.
