Answer: The running time should at least 119.32 seconds to be in the top 5% of runners.
Step-by-step explanation:
Let X= random variable that represents the running time of men between 18 and 30 years of age.
As per given, X is normally distrusted with mean [tex]\mu=93\text{ seconds}[/tex] and standard deviation [tex]\sigma=16\text{ seconds}[/tex].
To find: x in top 5% i.e. we need to find x such that P(X<x)=95% or 0.95.
i.e. [tex]P(\dfrac{X-\mu}{\sigma}<\dfrac{x-93}{16})=0.95[/tex]
[tex]P(Z<\dfrac{x-93}{16})=0.95\ \ \ \ \ [Z=\dfrac{X-\mu}{\sigma}][/tex]
Since, z-value for 0.95 p-value ( one-tailed) =1.645
So,
Hence, the running time should at least 119.32 seconds to be in the top 5% of runners.
