If you enter normalcdf(0, 13.5, 13.56, 2.24) in a calculator and the output result is the answer. Note that "0" is the lower limit, "13.5" is the upper limit, 13.56 is the mean, and 2.24 is the standard deviation. Less than 13.5 seconds means 0 is the lower limit and 13.56 is the upper limit.
Answer:
P(X< 13.5) = 0.834
Step-by-step explanation:
Given data:
mean of race time is [tex]\mu = 13.56[/tex]
standard deviation is [tex]\sigma = 2.24 seconds[/tex]
we know that z is given as [tex]= \frac{x-\mu}{\sigma}[/tex]
where x is 13.5 in given problem
so probability of having runner time less than 13.5
[tex]P(X< 13.5) = P(z< \frac{13.5 - 13.56}{2.24})[/tex]
P(X< 13.5) = P(z< -0.026)
P(X< 13.5) = P(z>(1 -0.026))
P(X< 13.5) = P(z > 0.974)
from standard z table , for z = 0.974 we have 0.834
P(X< 13.5) = 0.834
