April 2012 number 1

The following 24 observations give the length of time (in hours, ordered) for which a specific fully charged laptop computer will operate on battery before requiring recharging. 1.2 1.4 1.5 1.6 1.7 1.7 1.8 1.8 1.9 1.9 2.0 2.0 2.1 2.1 2.1 2.2 2.3 2.4 2.4 2.5 3.1 3.6 3.7 4.5 The owner of this computer is about to watch a film on his fully charged laptop. Calculate from these data the longest showing time for a film that he can watch, so that the probability that the battery's lifetime will be sufficient for watching the entire film is 0.75. [3]

The solution used the lower quartile ? I thought probability of 0.75 is the third quartile.
Please help to explain why lower quartile was used

 

Hi
We have P(X>L) = 0.75
So, P(X<L) = 0.25 here L is the lower quartile
Remember we need X to be less than Lower quartile for prob. 0.25 , not greater than.

 

We want to have a 75% chance of the battery lasting through that length of time.

By choosing the upper quartile, we have a 25% chance of the battery lasting LONGER than that time, and a 75% chance of the battery lasting LESS than that time.

By choosing the lower quartile, we have a 25% chance of the battery lasting LESS than that time, and a 75% chance of the battery lasting LONGER than that time.

Mathematically, P (t > film length) = 75%, so we need 75% of the values to be greater than that time, therefore choose the lower quartile value as 75% of values are greater than it.

Hope that helps. =)