The average commute to work one way is 25 minutes according

The average commute to work (one way) is 25 minutes according to the 2005 American Community Survey. If we assume that commuting times are normally distributed and that the standard deviation is 6.1 minutes, what is the probability that a randomly selected commuter spends more than 30 minutes commuting one way?

Select one:

a. 0.79

b. 0

c. 1

d. 0.21

e. Cannot be determined

Solution

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    30      
u = mean =    25      
          
s = standard deviation =    6.1      
          
Thus,          
          
z = (x - u) / s =    0.819672131      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   0.819672131   ) =    0.206201521 = 0.21 [ANSWER, OPTION D]