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# Answer to Question #15439 in Statistics and Probability for Sean

Question #15439
Unysis.com Is one of the most frewuented business to business web sites. Assuming that the duration of a visit to this website is normally distributed with a mean of 65.7 minutes and a standard deviation of 15 minutes Question : Less than how many minutes will only 20% of the visits last?
1
2012-09-27T10:40:47-0400
less than 20% correspond to z-score of -0.84. So the answer is
65.7+15*(-0.84)=53.08. So it&#039;ll last less than 53.08 min.

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Assignment Expert
11.10.12, 19:30

Actually that's not Sean)
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Vinay
11.10.12, 17:59

Assignment Expert
11.10.12, 17:17

For that you need to use table for standard normal distribution.
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The standard normal distribution table provides the probability that random variable x is less than or equal to z. In the table we have values of z>0(the very left column).For example, if we need to find& Φ(1.5) then we find “1.5” in the very left column of the table, pick the value of function which stands next to it
Returning to our problem, why is z=-0.84?
We& know that 20% of the observations (20% of the area under the curve) lie to the left of z. This value of z is obviously negative, because we see that zero point divides curve into equal parts, i.r. 50% of the area lies to the left of z=0. Also we can see that there’s no negative values of z in the table. But it’s evident that required value of z equals minus {z corresponding to 80%}. So let’s find z for which 80% of the curve area lies to the left.
To begin it helps to identify approximately where this value might be. Since 20% of the area under the curve must be to the right of z , z must be above 0.
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Since this problem begins in an opposite fashion, you might guess the procedure for a solution works in the opposite order.
We already know an area under the curve. However, the area we know is above the region to the right of z. The table handles areas under the curve to the left of values. The area under the curve over the region left of z is 0.8000. (Or...given that 20% of the values are to lie above z, it must be the case that 80% of the values lie below z.)
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Reverse the steps used previously.
Look up an area of 0.8000. Areas are found on the inside of the table. There is no value exactly equal to 0.8000, choose the closest one& 0.7995.
Now, from the margins, find the value z that accompanies this area. That value is 0.84.
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In our case therefore we have z=-0.84

vinay
10.10.12, 22:06

I would like to know how did you get the answer of -0.84 in the workings?

Assignment Expert
28.09.12, 15:19

If you really liked our service please press like-button beside answer field. Thank you!

Sean
27.09.12, 21:41

Thank you so much I was having doubts as to the 0.84 was negative or positive