The normal distribution mentioned in the problem can be understood as a function f(t) where t is in seconds.
We need to find the Z-score formula shown below
[tex]Z=\frac{x-\mu}{\sigma}[/tex]Where mu is the mean and sigma is the standard deviation.
In our case,
[tex]\begin{gathered} x=83,\mu=78,\sigma=2.5 \\ \Rightarrow Z=\frac{83-78}{2.5}=\frac{5}{2.5}=2 \end{gathered}[/tex]The corresponding probability to a Z-score equal to 2 can be found using a Z-score table. Z=2 -> 0.9972
Then, the answer is
[tex]42\cdot0.9972=41.8824\approx42[/tex]Then, the answer is approximately 42 trials
