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

In summary, the safety limits for tyres are between 1.9 − b bars and 1.9 + b bars. It is known that 80% of tyres are within these safety limits. The answer sheet is getting ± 1.282 from .8.
  • #1
mutineer123
93
0

Homework Statement


http://www.xtremepapers.com/CIE/International%20A%20And%20AS%20Level/9709%20-%20Mathematics/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%20A%20And%20AS%20Level/9709%20-%20Mathematics/9709_s05_ms_6.pdf)




Homework Equations





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?
 
Physics news on Phys.org
  • #2
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
tal444 said:
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.

Yeah I don't 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
mutineer123 said:

Homework Statement


http://www.xtremepapers.com/CIE/International%20A%20And%20AS%20Level/9709%20-%20Mathematics/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%20A%20And%20AS%20Level/9709%20-%20Mathematics/9709_s05_ms_6.pdf)


Homework Equations



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?


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
Ray Vickson said:
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
Okay, so you're breaking up the inequality into two inequalities. smart. Thank you!
 
Last edited:

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

1. What is a normal distribution?

A normal distribution is a probability distribution that describes how values are spread around a central mean value. In a normal distribution, most values are clustered around the mean, with fewer values appearing further away from the mean.

2. How is a normal distribution used in AS level statistics?

In AS level statistics, a normal distribution is used to model data that follows a bell-shaped curve. This allows for the calculation of probabilities and confidence intervals for a given set of data.

3. Can you explain the last part of the tyre problem?

In the last part of the tyre problem, you are likely being asked to use the normal distribution to calculate the probability of a tyre lasting for a certain number of miles. This involves finding the z-score for the given mileage and using a z-table to find the corresponding probability.

4. How do you calculate the z-score for a given data point?

The z-score for a given data point can be calculated by subtracting the mean from the data point and then dividing that difference by the standard deviation. This gives you a standardized value that can be used to find the corresponding probability on a z-table.

5. What is the purpose of using the normal distribution in this tyre problem?

The normal distribution is used in this tyre problem to model the data and calculate the probability of a tyre lasting for a certain number of miles. This allows us to make informed decisions about the likelihood of a tyre lasting for a given distance and make predictions about the durability of the tyres.

Back
Top