Solution:
Given:
[tex]\begin{gathered} \mu=4\text{ minutes} \\ \sigma=3\text{ minutes} \\ x=1\text{ minute} \end{gathered}[/tex]
Using the Z-score formula, the Z-score of the data is gotten below.
[tex]Z=\frac{x-\mu}{\sigma}[/tex]
Hence,
[tex]\begin{gathered} Z=\frac{1-4}{3} \\ Z=\frac{-3}{3} \\ Z=-1 \end{gathered}[/tex]
From the Z-scores table, the probability that a person will wait for more than 1 minute is;
[tex]\begin{gathered} P(x>Z)=0.84134 \\ \\ To\text{ four decimal places;} \\ P(x>Z)=0.8413 \end{gathered}[/tex]
Therefore, to four decimal places, the probability that a person will wait for more than 1 minute is 0.8413
