My Math Forum statistic. how do I get this answer?

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 February 19th, 2014, 02:20 AM #1 Senior Member   Joined: Nov 2011 Posts: 101 Thanks: 0 statistic. how do I get this answer? The diameters of bearing journals ground on a particular grinder can be described as normally distributed with mean 2.0005 in. and standard deviation .0004 in. (a) If engineering specifications on these diameters are 2.0000 in. +/- .0005 in, what fraction of these journals are in specifications? answer is 0.4938 but how do you get this answer from this? i am totally lost and the book has not a single example or steps to solve this problem. how do they expect anyone to solve this when they don't show example problems that's similar to this? i've been on this 8 hours already and about to go crazy. please help.
 February 19th, 2014, 03:34 AM #2 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 Re: statistic. how do I get this answer? The upper limit on the "specification" is 2.0000+ 0.0005= 2.0005, exactly the mean of your normal distribution. Without consulting a table, you should recognize that 50% of the normal distribution is below the mean. The lower limit is 2.0000- 0.0005= 1.9995. That is 2.0005- 1.9995= 0.0005 below the mean which is 0.0005/0.0004= 1.25 standard deviations below the mean. Looking at a table of the normal distribution (a good one is at http://www.stat.duke.edu/~banks/111-FAQ ... tTable.pdf) but you should have one in your text book) 1.25 standard distributions below the mean (-1.25) has probability 0.1056. So the probability the true value is between those two limits is 0.5000- 0.1056= 0.3944. I would be very surprised if your text book had no examples of that. Perhaps you mean that your text has no examples of calculating the probability. That would be because, while it is possible to calculate, it would involve tedious numerical calculations (essentially, a numerical integration) which is why we don't "calculate" them- we use a table where they have already been calculated by machine. What is the title of the text book?

### the diameters of bearing journals ground on a particular grinder

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