Question

The average time it takes to commute to work (one-way) in the U.S. is 25.1 minutes. Assume these commute times follow a normal probability distribution with a standard deviation of 11.3 minutes. Ninety-eight percent of all commutes to work take less than what time?

Answer 1

The given percentage is 98%

This is equivalent to 0.98

First find P(Z>0.98)

This gies:

`P(z<0.98)=2.054`

Uing the score formula:

`z=(x-\mu)/(\sigma)`

Substitute z=2.054 and the given values:

`2.054=(x-25.1)/(11.3)`

Solve the equation for x:

`\begin{gathered} 23.21=x-25.1 \\ 23.21+25.1=x \\ x=48.31 \end{gathered}`

Therefore the required answer is 48.31 minutes.