Question

The amount of cereal in a box is normally distributed with a mean of 24 oz. and a standarddeviation of 0.62 oz. If 7,500 boxes of cereal are packaged in one day, approximately how many boxeswould contain less than 22.9 oz.?

Answer 1

Given data:

The given mean is m=24.

The given standard devaition is s=0.62.

The given vallue is x=22.9.

The expression for the value of z is,

`\begin{gathered} P(x<22.9)=P(z<(x-m)/(s)) \\ =P(z<(22.9-24)/(0.62)) \\ =P(z<-1.774) \end{gathered}`

Refer the standard z-table.

`P(x<22.9)=0.03836`

The number of box required are,

`\begin{gathered} N=7,500*0.03836 \\ =287.7 \\ \approx288 \end{gathered}`

Thus, the number of boxes are 288.