1. ## Probability and Statistics (Check My Answer)

Hi guys, i was given the following problem:

The mean diameter of a batch of bolts is 9.711mm and the standard deviation of the batch is 0.126mm

The tolerance for this batch of components is 9.73mm to 9.97mm.
In a batch of 2000 bolts, determine the following:

a) The percentage of bolts rejected assuming the bolts are normally distributed.

(9.97 - 9.73) / 0.126 = 1.90

1.90 Corresponds to: 0.9713

1 - 0.9713 = 0.0287

(Little less than 3% are rejected)

0.0287 x 2000 = 57.4

= 57 rejected out of 2000

Can anybody tell me if i'm right?

2. Originally Posted by c00ky
Hi guys, i was given the following problem:

The mean diameter of a batch of bolts is 9.711mm and the standard deviation of the batch is 0.126mm

The tolerance for this batch of components is 9.73mm to 9.97mm.
In a batch of 2000 bolts, determine the following:

a) The percentage of bolts rejected assuming the bolts are normally distributed.
I do not follow what you are doing.
---
Those that are accepted is,
$\displaystyle P(9.73\leq x\leq 9.97)=$$\displaystyle P(9.711\leq x\leq 9.97)-P(9.711 \leq x\leq 9.73)$
Find the z-scores
$\displaystyle \frac{9.97-9.711}{.126}\approx 2.06$
$\displaystyle \frac{9.73-9.711}{.126}=.0019$
Thus, now find,
$\displaystyle 2.06-.0019=2.041$
Find this on a chart, 47.93%
Thus, the precentage that those that are rejected is, 52.07&
Thus, out of 2000 bolts 52% are rejected: 1041

3. You need the area to the right of 9.97 and the area to the left of 9.73.

The area in between is what you keep because anything less than 9.73 or greater than 9.97 is rejected.

$\displaystyle \frac{9.97-9.711}{0.126}=2.055$

$\displaystyle \frac{9.73-9.711}{0.126}=0.15$

2.055 corresponds to 0.98 and 0.15 corresponds to 0.5596

You need the area to the right of 9.97 so subtract 0.98 from 1 and get 0.02.

You need the area to the left of 0.15 so you need 0.5596.

Also, you could look at it this way:

Count up the region you keep and subtract it from 1:

(0.98-0.5596)=0.4204; 1-0.4204=0.5796=58% rejected. Same thing.