A manufacture of metal washer turn out washer with a mean of 4.5 g and a standard deviation of 0.047g, what is the probability that a randomly selected washer wall have a mass lees than 4.58g?

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- Jun 2nd 2007, 01:28 PMbrandyhelp:( with standard deviation
A manufacture of metal washer turn out washer with a mean of 4.5 g and a standard deviation of 0.047g, what is the probability that a randomly selected washer wall have a mass lees than 4.58g?

- Jun 2nd 2007, 05:42 PMThePerfectHacker
Find the z-score:

$\displaystyle z=\frac{4.58 - 4.5}{.047} \approx 1.7$

Look up on Statistics tables the corresponding value which is $\displaystyle .4554$.

So $\displaystyle P(4.5\leq x \leq 4.58) = .4558$

Thus,

$\displaystyle P(x\leq 4.58) = P(x\leq 4.5)+P(4.5\leq x\leq 4.58) = .5+.4558 = .9558$ - Jun 3rd 2007, 02:31 AMCaptainBlack
There is a slight problem here in that there is no standard for how tables

of the standard normal distribution are presented.

Now**Im**PerfectHackers table gives the probability that X takes a value

between 0 and z (>0). However another common form of table

gives the probability that X takes a value between -infty and the z, that

is it is a table of the cumulative standard normal.

If you use a software package to do this sort of thing the function used

to give the probability will usually be like the second of the forms of table

described rather than the former.

RonL - Jun 4th 2007, 02:57 PMbrandyI dont understand :(
I am so confused can you explain to me? :eek: :o :eek:

- Jun 4th 2007, 03:15 PMThePerfectHacker
- Jun 4th 2007, 04:19 PMbrandywhere...
where did the .5 come from? I am not to sure? thanks!

- Jun 4th 2007, 05:59 PMThePerfectHacker
First I wrote $\displaystyle P(x\leq 4.58) = P(x\leq 4.5)+P(4.5\leq x \leq 4.58)$

Now, $\displaystyle P(4.5\leq x\leq 4.58) = .4558$ because that was derived from the z-score.

And $\displaystyle P(x\leq 4.5)=.5$ because it is the area of everything on the left hand side of the mean. Thus it is exactly 1/2.