Answer:
The probability is [tex]P(X > x) = 0.0013499[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 25[/tex]
The standard deviation is [tex]\sigma = 5 \ minutes[/tex]
The random number [tex]x = 40[/tex]
Given that the time taken is normally distributed the probability is mathematically represented as
[tex]P(X > x) = P[\frac{X -\mu}{\sigma } > \frac{x -\mu}{\sigma } ][/tex]
Generally the z-score for the normally distributed data set is mathematically represented as
[tex]z = \frac{X - \mu}{\sigma }[/tex]
So
[tex]P(X > x) = P[Z > \frac{40 -25}{5 } ][/tex]
[tex]P(X > x) = 0.0013499[/tex]
This value is obtained from the z-table
