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,
[tex]\begin{gathered} P(x<22.9)=P(z<\frac{x-m}{s}) \\ =P(z<\frac{22.9-24}{0.62}) \\ =P(z<-1.774) \end{gathered}[/tex]Refer the standard z-table.
[tex]P(x<22.9)=0.03836[/tex]The number of box required are,
[tex]\begin{gathered} N=7,500\times0.03836 \\ =287.7 \\ \approx288 \end{gathered}[/tex]Thus, the number of boxes are 288.
