# Math Help - Chi Square test and Failure Rate Questions

1. ## Chi Square test and Failure Rate Questions

[/SIZE][/FONT] Given a target mean of 100, a standard deviation of 1 when the process is in control, and the product is acceptable between the range of 97 to 103. A measurement outside this range is a failure.

If the process is in control, how many failures do you expect out of every 10,000 items produced?

2. Is that 97 to 103 a 95% confidence interval for the mean?

3. it doesnt say, thats all the information it gives you.

4. O.K. Its been a while since I did a quality control course (assuming that is what you are doing?) but you could work backwards to find an initial n using the rule for a confidence interval and then determine if this sample size is big enough to map back to n= 10,000.

5. to calculate the z value i used 103 = 100+z(SD/SQRT(n)) => 3 = z(1/100) => z = 300 which doesnt make much sense to me.

6. I think there's more to the question than what I can offer at this point (unless I starting digging through my undergrad notes) but if this is a 95% confidence interval then

$\displaystyle 103 = 100 + 1.96 \times \frac{1}{\sqrt{n}}$ then solve for $n$

7. yea that doesnt work sorry. the answer is 26 tho if that helps.