Math Problem!

lkavo

I am trying to study for a maths test that I have coming up shortly but I am stuck on one f the questions:

The lengths (in seconds) of advertisements aired by a television chan- nel are normally distributed with mean 150 seconds and standard de- viation 22 seconds. What proportion of advertisements are:
(i) shorter than 170 seconds

If anyone could help me or point me towards a website that can help it would be great!

Thanks

Delphi91

lkavo wrote: »

I am trying to study for a maths test that I have coming up shortly but I am stuck on one f the questions:

The lengths (in seconds) of advertisements aired by a television chan- nel are normally distributed with mean 150 seconds and standard de- viation 22 seconds. What proportion of advertisements are:
(i) shorter than 170 seconds

If anyone could help me or point me towards a website that can help it would be great!

Thanks

Off the top of my head, a back of an envelope calculation would be as follows:

IIRC, 68% of a normal distribution lies between the mean +/- one standard deviation i.e. between 128 seconds and 172 seconds. Give the symmetry of a normal distribution, that would mean that 16% are below 128 seconds and 16% are above.

Therefore, an approximate % less than 172 seconds is 16 + 68 = 84%. The correct answer will be a little less than this.

Have a look here: http://www.mathportal.org/calculators/statistics-calculator/normal-distribution-calculator.php - it gives the probability of the ad being less than 170 seconds of 0.8186 i.e. 81.86% of ads are less than 170 seconds.

lkavo

Thanks for the help