# Standard Deviation

• Jun 7th 2009, 07:32 PM
dan123
Standard Deviation
Krina works in a call centre assisting home computer systems. The average length of a call in her centre is 605 seconds. Her last call took 569 seconds. Her manager offeres a bonus for calls that are handled quickly. If a call is handled quicker than 95% of calls,a 2 dollar bonus is paid. What is the largest standard deviation for calls that would let Krinas latest call get the bonus?
• Jun 7th 2009, 07:37 PM
mr fantastic
Quote:

Originally Posted by dan123
Krina works in a call centre assisting home computer systems. The average length of a call in her centre is 605 seconds. Her last call took 569 seconds. Her manager offeres a bonus for calls that are handled quickly. If a call is handled quicker than 95% of calls,a 2 dollar bonus is paid. What is the largest standard deviation for calls that would let Krinas latest call get the bonus?

What distribution does the call length follow?
• Jun 7th 2009, 07:38 PM
dan123
does not say,I am pretty sure it would be normal wouldn't it?
• Jun 7th 2009, 07:51 PM
mr fantastic
Quote:

Originally Posted by dan123
does not say,I am pretty sure it would be normal wouldn't it?

You're probably meant to assume the rule of thumb that approximately 95% of the values will lie within two standard deviations of the mean .... In which case (making several assumptions) you require $(605 - 569) = 2 \sigma$.
• Jun 7th 2009, 07:52 PM
dan123
so you would have to figure out the standard deviation?
• Jun 7th 2009, 07:54 PM
mr fantastic
Quote:

Originally Posted by dan123
so you would have to figure out the standard deviation?

Yes, from the equation I gave you.
• Jun 7th 2009, 08:10 PM
dan123
so the standard deviation would be 18,but one thing I just don't get is its out of four marks,I couldn't see that simple equation being enough for four marks haha,some of the marking amounts on these questions just don't make sense
• Jun 7th 2009, 08:16 PM
mr fantastic
Quote:

Originally Posted by dan123
so the standard deviation would be 18,but one thing I just don't get is its out of four marks,I couldn't see that simple equation being enough for four marks haha,some of the marking amounts on these questions just don't make sense

Possible marking scheme at the elementary level:

Statement: Approximately 95% of the values will lie within two standard deviations of the mean .... 1 mark

Correct equation: $(605 - 569) = 2 \sigma$ .... 2 marks

Correct solution to equation: $\sigma = 18$ .... 1 mark