standard deviation?

[bpilgrim]

i have a question i need to do for a "chapter check". can you push me in the right direction? i don't know where to start with this one.

"Adrianna works in a warehouse that supplies a variety of goods to online shoppers. Depending how fast Adrianna processes the orders, she will receive a $4 bonus (only if an order is processed faster than 91% of all orders). On average, processing orders at the warehouse takes 300 seconds and the last order Adrianna placed lasted only 264 seconds."

the question is: "In order for Adrianna to receive her $4 bonus on her most recent order, what is the largest standard deviation that would make this possible?"

 

[galactus]

In order to receive the bonus, Adrianna must be in the 91st percentile. That is, she processed faster than 91% of the other processors. Look up the z-score that corresponds to .91 in the body of the z-table. Then, use:

\(\displaystyle z=\frac{x-{\mu}}{\sigma}\) and solve for \(\displaystyle {\sigma}\).

 

[bpilgrim]

Thnx. So it would be:

0.8186 = 264-300/standard dev. ?

 

[chrisr]

No, that's not it,
you have looked up a z-score of 0.91 and read off that this corresponds to about 82%.

You must read the z-score that corresponds to 91% or 0.91 or 9% or 0.09.
The z-score is the amount of standard deviations from the mean.

Your z = (264-300)/(SD) is negative.

You could find the z-value that corresponds to the "quickest 9%" of processings or the slowest 9% of processings,
since if the probability distribution follows the normal curve, then it's symmetrical about the mean,
which corresponds to z=0 on the standard normal curve.

Hence, your reading should be z = 1.34 or -1.34.

The largest standard deviation corresponds to these values, as smaller ones will correspond to even higher percentiles above 91%
or lower than 9%.

That's how you find the largest standard deviation in this case. (It's called a one-tailed test).