Q:

# 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?

Accepted Solution

A:
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 ΞΌ and a standard deviation of Ο is less than a value, x, is given by:

$$P(X\ \textless \ x)=P\left(z\ \textless \ \frac{x-\mu}{\sigma} \right)$$

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:

$$P(X\ \textless \ 18)=P\left(z\ \textless \ \frac{18-25}{6.1} \right) \\ \\ =P(z\ \textless \ -1.148)=\bold{0.1256}$$