# normal distribution question

• Apr 12th 2010, 08:30 PM
shawli
normal distribution question
A machine is set to manufacture circular metal discs of diameter $10 cm$; in fact, the diameter (in cm) of the discs it produces is a random variable $Y$ with normal distribution having a mean of $10.05$ and a standard deviation of $0.10$.
The demand of quality control place "acceptable limits between $9.90 cm$ and $10.20 cm$; all disks out of this range are rejected.

a) Given that a particular disk is accepted, find the probability that its diameter is more than $10 cm$.

b) It is decided that too many discs are rejected by the standard. If a new rejection rate is to be 10%, find the new acceptable limits, equally spaced on either side of the mean.

c) Use the fact that $Var(Y) =E(Y^2) - [E(Y)]^2$ to estimate the mean area of the discs.
• Apr 15th 2010, 12:55 AM
dkmathguy
a) $

P\left(10 \leq X \leq 10.20\right) ?

$

b) $
P\left(A \leq X \leq B \right) = 0.9 ?
$

Where 10.05 - A = B - 10.05