# A normal distribution problem, AS level, on tyres! Need help in the last part.

1. Mar 27, 2012

### mutineer123

1. The problem statement, all variables and given/known data
http://www.xtremepapers.com/CIE/International A And AS Level/9709 - Mathematics/9709_s05_qp_6.pdf

question no. 6 part ii (Safety regulations state that the pressures must be between 1.9 − b bars and 1.9 + b bars. It is
known that 80% of tyres are within these safety limits. Find the safety limits)

My answer is not matching anywhere near the right answer (http://www.xtremepapers.com/CIE/International A And AS Level/9709 - Mathematics/9709_s05_ms_6.pdf)

2. Relevant equations

3. The attempt at a solution

I used .8 as my probability for which the Z value is .842
Then I standardised my X values to Z, so i got P( -b/0.15< Z < b/.15) =0.8

Computing that i got .06315 as my b value.

Where is the answer sheet getting ± 1.282 from?

2. Mar 27, 2012

### tal444

Your probability is 0.80, but remember, this is the area in the middle, not from one end of the normal distribution curve.

Hint: Your 80% is centered around 1.9, so what are the probabilities of each end that is NOT within the safety limits. After that, all you need is the invNorm function on your calculator.

EDIT: Woah, on second thought, I'm not sure what method you and the answer sheet use. Maybe my way isn't the way you were taught. However, I know for sure it works.

3. Mar 27, 2012

### mutineer123

Yeah I dont know the method with the "invNorm function".
Regarding the hint "Your 80% is centered around 1.9", yes i have taken that into account. Since the rane as i stated was -b/0.15< Z < b/.15. I first formed an equation for the probability where Z< b/0.15. Then I formed a probability of Z< -b/0.15. Now I deduct the 2 probabilities(their equations actually) to get the actual probability, the resultant equation in b(which like you said is centered) Now this resultant equation is 0.8. So I solve for b. But apparently it is wrong.

4. Mar 28, 2012

### Ray Vickson

You need 10% probability of {Z < -zc} and 10% probability of {Z > zc}, so zc = 1.28155. Thus, b/0.15 = zc = 1.28155, so b = 0.192.

RGV

5. Mar 29, 2012

### mutineer123

Okay, so you're breaking up the inequality into two inequalities. smart. Thank you!

Last edited: Mar 29, 2012