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?
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?
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,
$\displaystyle P(x\leq 4.58) = P(x\leq 4.5)+P(4.5\leq x\leq 4.58) = .5+.4558 = .9558$
There is a slight problem here in that there is no standard for how tables
of the standard normal distribution are presented.
Now ImPerfectHackers 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
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.