Explanation
We are given the following information:
[tex]\begin{gathered} mean(\mu)=11.6 \\ standard\text{ }deviation(\sigma)=2.6 \end{gathered}[/tex]We are required to determine the probability that the item purchased will last longer than 4 years.
This is achieved thus:
We know that we can standardize the normal distribution using the formula:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]Therefore, we have:
[tex]\begin{gathered} P(X>4)=P(Z>\frac{4-11.6}{2.6}) \\ =P(Z>-2.923) \\ =0.99827 \end{gathered}[/tex]Hence, the answer is:
[tex]\begin{equation*} 0.99827 \end{equation*}[/tex]