ANSWER
0.9738 or 97.38%
EXPLANATION
Given:
[tex]\begin{gathered} mean(\mu)=6.9 \\ Standard\text{ }Deviation(\sigma)=1.6 \end{gathered}[/tex]Desired Outcome:
Probability that it will last 10 years
z-score for the sample:
[tex]\begin{gathered} z-score=\frac{X-\mu}{\sigma} \\ z-score=\frac{10-6.9}{1.6} \\ z-score=1.9376 \end{gathered}[/tex]p-value
For the z-score of 1.9376, the p-value is 0.9738 or 97.38%
Hence, the probability that it will last longer than 10 years if you randonly purchase one item is 97.38%