MATH SOLVE

4 months ago

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:

[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]

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:

[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]