Given that 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 less
than 18 minutes commuting one way
The probability that a randomly selected number from a normally distributed dataset with a mean of μ and a standard deviation of σ is less than a value, x, is given by:
[tex]P(X\ \textless \ x)=P\left(z\ \textless \ \frac{x-\mu}{\sigma} \right)[/tex]
Given that the average commute time to work (one way) is 25 minutes and that the standard deviation is 6.1 minutes,
the
probability that a randomly selected commuter spends less than 18
minutes commuting one way is given by:
[tex]P(X\ \textless \ 18)=P\left(z\ \textless \ \frac{18-25}{6.1} \right) \\ \\ =P(z\ \textless \ -1.148)=\bold{0.1256}[/tex]
