Let x denote the time it takes to run a road race Suppose x

Let x denote the time it takes to run a road race. Suppose x is approximately normally distributed with a mean of 190 minutes and a standard deviation of 21 minutes. If one runner is selected at random, what is the probability that this runner will complete this road race in less than 152.20 minutes?

Round the answer to 4 decimal places.

Solution

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    174.5      
u = mean =    150      
          
s = standard deviation =    10.24695077      
          
Thus,          
          
z = (x - u) / s =    2.390955178      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2.390955178   ) =    0.008402302 [ANSWER]