Question

The average commute time to work (one way) is 25 minutes according to the 2005 american community survey. if we assume that commute 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?

Answer 1

We have

Mean, μ = 25 minutes
Standard Deviation, σ = 6.1
X = 30 minutes

The probability we are looking for is shown in the first diagram; it's the area on the right of X=30

We need to standardized the value X=30 using the formula $\frac{X-mean}{standard deviation}$
$\frac{30-25}{6.1}=0.82$ rounded to two dp

The z-table is shown on the second diagram only gives the probability when P(Z<z), so to work out the probability when P(Z>z), we do 1-P(Z<z)

P(Z>0.82) = 1 - P(Z<z) = 1 - 0.7939 = 0.2061