Posted: 11/28/2009 12:25:19 PM EDT
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My wife has some questions on some problems and I don't have a clue as I haven't dealt with this stuff in years. She is not sure of the process for these two:
The lengths of time bank customers must wait for a teller are normally distributed, with a mean of 3 minutes and a SD of 1 minute. a.What proportion of the bank customers waits between 3 and 4.5 min b.What percentage wait more than 4 minutes c.What proportion waits between 2 and 3.5 minutes d.What percenatage waits less than a minute Forty percent of a population have a blood type O. Find the following probabilities for a random sample of 80 people. a. More than 25 have blood type O b. More than 40 have blood type O c. Fewer than 35 have blood type O Between 30 and 36 have blood type O She needs just some help on how to get started and the process. Thanks!! |
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Quoted:
http://upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Standard_deviation_diagram.svg/325px-Standard_deviation_diagram.svg.png Normal distribution curve. How is she supposed to solve these problems? By using the normal curve shown above? Or can she use a TI? I can post the steps on the TI if her instructor is OK with her using that. |
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Quoted: Quoted: How is she supposed to solve these problems? By using the normal curve shown above?http://upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Standard_deviation_diagram.svg/325px-Standard_deviation_diagram.svg.png Normal distribution curve. Or can she use a TI? I can post the steps on the TI if her instructor is OK with her using that. I was just looking for the correct procedure for distribution curve questions and came across that diagram. No, on its own it will not "help" to solve the problem but it is relevant to the thread and should help some people to visualize what's going on. That was my reasoning anyway. |
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Quoted: Total area of the curve is 1. http://en.wikipedia.org/wiki/Standard_score http://www.science.mcmaster.ca/psychology/poole/z-table2.jpg This is what I was looking to post! Good find!  |
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Quoted: That curve has the percentages. You have the mean and SD, that curve is all you need for the first problem (with a little guess).Quoted: Quoted: How is she supposed to solve these problems? By using the normal curve shown above?http://upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Standard_deviation_diagram.svg/325px-Standard_deviation_diagram.svg.png Normal distribution curve. Or can she use a TI? I can post the steps on the TI if her instructor is OK with her using that. I was just looking for the correct procedure for distribution curve questions and came across that diagram. No, on its own it will not "help" to solve the problem but it is relevant to the thread and should help some people to visualize what's going on. That was my reasoning anyway. I don't remember any stat package for the TI other than maybe an add-on––that will do a Gaussian distribution. |
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You never did say if she is allowed to use her calculator. We always could. This is from my old notes (TI-83 Plus):
2nd, distr, 2:normalCDF (Lower boundary, Upper boundary, mean, standard deviation) For example, problem 1a would be: 2nd, distr, 2:normallCDF (3,4.5,3,1) I hope she's figured it out by now. |
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Quoted: The PDF is http://upload.wikimedia.org/math/e/5/3/e53cbc1bba1bc3dd795416d27ed2d612.png (from Wikipedia). Integrate it between the bounds you are interested in. No need to do any calculus for this at all. For example first problem part B. You just need to calculate the standard score  so X is the value you are interested in 4 minutes, mu= mean which is 3, sigma is 1 so z = (4-3)/1 = 1 z=1 Look it up in the table. It will give you the percentage. Assuming i did the math right in my head it should be something like 16% for part b. |
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If shes gonna be dealing with large data sets at its worth looking into minitab, I'll reemphasize that. It's probably the most popular and powerful statistical software on the market. Schools sometimes have limited licenses that they provide free or low cost for students. |
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Quoted: The PDF is http://upload.wikimedia.org/math/e/5/3/e53cbc1bba1bc3dd795416d27ed2d612.png (from Wikipedia). Integrate it between the bounds you are interested in. Integration of the Normal PDF is not for the faint-hearted. Or even most of the stout-hearted. Use a table, or a stats package. |
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I can probably work them out on paper and post step by step solutions tonight if that's not too late. I have some errands I need to do. It's really a matter of understanding how to interpret the normal distribution and how it relates to z-scores. It's important to under stand that for a normal distribution the entire area under the curve is 1 as in 100%. The mean is a point of symmetry obviously and .5 or 50% of the data is on either side of it. When you find a z-score that score is the point along the curve that means a certain percent lies between the bounds established by the table. Now some tables are values for say everything to the left of z or right of z or within the bounds established between z and the mean. You gotto look at the table and it will have a pictograph, and usually a short explanation showing a shaded area that the values represent. You may need to add or subtract depending on the table. The book should have its own table of z values and thats the one you should be using. |
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Quoted:
Total area of the curve is 1.
http://en.wikipedia.org/wiki/Standard_score http://img340.imageshack.us/img340/8458/teste.jpg Pffft, cheater. I was going to tell her to integrate the curve. 
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