Question

Commute Time to Work The average commute to work (one way) is 25 minutes according to the 2005 American Community Survey. If we assume thatcommuting times are normally distributed and that the standard deviation is 6.1 minutes, find the probabilities. (a) The selected commuter spends more than 28 minutes commutiP(x> 28) =

Answer 1

`\begin{gathered} X=28 \\ \mu=25 \\ \sigma=6.1 \\ Z=(X-\mu)/(\sigma) \\ Z=(28-25)/(6.1) \\ Z=0.4918 \\ \text{Hence} \\ P\mleft(X>28\mright)=P\mleft(Z>0.4918\mright)=0.3114\text{ } \\ \text{The probability is 0.3114 or 31.14\%} \end{gathered}`