# Help with one short problem.

• Feb 17th 2007, 11:34 PM
Math123
Help with one short problem.
1.The driving time for an individual from his home to his work is distributed between 300 to 480 seconds.
So here are the two things I need to solve for this problem:

Compute the probability that the driving time will be less than or equal to 435 seconds.
Determine the expected driving time and its standard deviation.

How can I do this? :confused:
• Feb 18th 2007, 12:47 AM
CaptainBlack
Quote:

Originally Posted by Math123
1.The driving time for an individual from his home to his work is distributed between 300 to 480 seconds.
So here are the two things I need to solve for this problem:

Compute the probability that the driving time will be less than or equal to 435 seconds.
Determine the expected driving time and its standard deviation.

How can I do this? :confused:

First as you have typed the question there is no answer as you have not specified a distribution. But lets assume you mean uniformly distributed between 300 and 480 seconds.

Probability that travelling time is less than 435 is:

integral (p(x) dx, x=-inf,435) = integral (1/180) dx, x=300,435)

as p(x)=(1/180) for x in (300, 480), and 0 otherwise.

integral (p(x) dx, x=-inf, 435) = integral (1/180) dx, x=300, 435)
............................. ..=(1/180) (435-300)=135/180 = 0.75

By definition the mean:

m = integral (x p(x) dx, x=-inf, inf) = integral (x/180 dx, x=300, 480)
.............................. ........=480^2/360-300^2/360 = 390.

The definition of SD:

s = sqrt(V),

V = integral ((x-m)^2 p(x) dx, x=-inf, inf)

which I will leave for you to do.

RonL
• Feb 18th 2007, 05:05 PM
Math123
I'm not getting it. :(
• Feb 18th 2007, 10:37 PM
CaptainBlack
Quote:

Originally Posted by Math123
I'm not getting it. :(

The uniform distribution between 300 and 480 has density:

p(x)=(1/180); x in (300, 480)
p(x)=0 otherwise.

Then you just use the text book definitions of the quatities you require
and compute the integrals.

p(x<a) = integral p(x) dx, x=-inf, a

mu= integral xp(x) dx, x=-inf, inf

var= integral (x-mu)^2 p(x) dx, x=-inf, inf

sigma=sqrt(var)

RonL