standard deviation?

bpilgrim

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Nov 24, 2009
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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?"
 
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 \(\displaystyle {\sigma}\).
 
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).
 
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