Respuesta :
Answer:
A) 30.6%
B) 420,500 batteries
Explanations:
A) First, we need to convert the range of number of hours to z-scores, this can be expressed as:
[tex]z=\frac{x-\overline{\mu}}{\sigma}[/tex]where
µ is the mean value
σ is the standard deviation
If the number of hours is 4120 hours, then the z-score will be;
[tex]\begin{gathered} z_1=\frac{4120-4000}{600} \\ z_1=\frac{120}{600} \\ z_1=0.2 \end{gathered}[/tex]If the number of hour is 4720 hours, then the z-score wil be;
[tex]\begin{gathered} z_2=\frac{4720-4000}{600} \\ z_2=\frac{702}{600} \\ z_2=1.2 \end{gathered}[/tex]The equivalent z-score will be;
[tex]0.2Find the equivalent probability[tex]\begin{gathered} P(0.2Hence the percentage of batteries that will last between 4120 and 4720 hours is 30.6%B) In order to determine the total batteries that will last up to 4600 hours if the there are 500,000 batteries, we will have;
[tex]\begin{gathered} z=\frac{4600-4000}{600} \\ z=\frac{600}{600} \\ z=1 \end{gathered}[/tex]Such that;
[tex]P(z<1)=0.8413=84.13\%[/tex]Find the required number of batteries
[tex]\begin{gathered} Total\text{ batteries<}0.8413\times500,000 \\ Total\text{ batteries}<420650batteries \\ Total\text{ batteries}=420,500 \\ \end{gathered}[/tex]Since 420,500 is less than the calculated, hence the total batteries that will last up to 4600 hours is 420,500 batteries
