Answer: 0.0668
Step-by-step explanation:
Given: Mean : [tex]\mu=\text{4 min. 3 sec.=4.05 minutes}[/tex]
Standard deviation : [tex]\sigma = \text{2 seconds=0.033333 minutes }[/tex]
The formula to calculate z-score is given by :_
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x= 4 minutes , we have
[tex]z=\dfrac{4-4.05}{0.03333}\approx-1.5[/tex]
The P-value = [tex]P(z\leq-1.5)=0.0668072\approx0.0668[/tex]
Hence, the probability that on a given run, the time will be 4 minutes or less = 0.0668
