Answer:
c = 89.4 seconds
The time for the fastest 10 % is less than 89.4 seconds
Step-by-step explanation:
The mean value is μ = 115 seconds and the standar deviation δ = 20 seconds.
We need to find c such that
P(x<c) = 0.1 It means, C is the time for the fastest 10 %
Such that:
[tex]z = \frac{c-\mu}{\sigma}[/tex]
[tex]z_{0.1} = \frac{c-115}{20}[/tex]
We find z of the normal standard table
[tex]z_{0.1} = -1.28\\[/tex]
Thus
[tex]-1.28 = \frac{c - 115 }{20}[/tex]
c = 89.4 seconds
The time for the fastest 10 % is less than 89.4 seconds
