The parameters provided from the question is:
[tex]\begin{gathered} \mu=886 \\ \sigma=\sqrt{8464}=92 \\ \bar{x}=904.8 \\ n=145 \end{gathered}[/tex]Using the z-score formula:
[tex]z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]Substitute for the values provided and solve for z
[tex]\begin{gathered} z=\frac{904.8-886}{\frac{92}{\sqrt{145}}} \\ z=2.4607 \end{gathered}[/tex]The probability that the main battery life will be greater than 904.8 is given:
[tex]\begin{gathered} P(z>2.4607)=P(0\leq z)-P(02.4607)=0.5-0.4931 \end{gathered}[/tex][tex]P(z>2.4607)=0.0069[/tex]Hence, the probability that the main battery life will be greater than 904.8 is 0.0069
