What is the probability of a cable having a breaking load greater than 6200 N?

In summary, the conversation discusses the calculation of the z-value and probability for a question involving a cable manufacturer and the breaking load of their cables. The probability that a randomly selected cable will have a breaking load greater than 6200 Newtons is determined to be 90%. There is also a discussion about reading from the stats table and understanding the standard normal curve.
  • #1
rexxii
11
0
TL;DR Summary
Probability - z value - stats issue
Hi,

I'm working on a question now where I need to calculate the z value. which I have been able to but I'm calculating a value off the normal distribution that is on the left-hand side of the normal distribution curve and it needs to on the right side. As the value I'm looking into is higher than the mean!

I cannot figure out how I would turn this around. its only one independent event there's no replacement or other variables.

the question is:

A cable manufacturer tests the cables it produces to find the breaking load. Over many years this has been assumed to be normally distributed with a mean of 6000 Newtons and standard deviation of 155 Newtons. Calculate the probability that a single cable chosen at random, will have a breaking load greater than 6200 N. Z = 6200 -6000 /155 = 1.29

Then I've written a probability statement (P z>1.290) = P z>1.290)

read from the stats tables that it could be 0.9015.

Said the breaking load is 90.15%

I know this is incorrect please can you advise The probability that a randomly selected cable will have a breaking load greater breaking load than 6200 Newtons is 90%.
 
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  • #2
rexxii said:
Summary: Probability - z value - stats issue

Hi,

I'm working on a question now where I need to calculate the z value. which I have been able to but I'm calculating a value off the normal distribution that is on the left-hand side of the normal distribution curve and it needs to on the right side. As the value I'm looking into is higher than the mean!

I cannot figure out how I would turn this around. its only one independent event there's no replacement or other variables.

the question is:

A cable manufacturer tests the cables it produces to find the breaking load. Over many years this has been assumed to be normally distributed with a mean of 6000 Newtons and standard deviation of 155 Newtons. Calculate the probability that a single cable chosen at random, will have a breaking load greater than 6200 N. Z = 6200 -6000 /155 = 1.29

Then I've written a probability statement (P z>1.290) = P z>1.290)

read from the stats tables that it could be 0.9015.
You're reading the table wrong. The table is giving you P(z < 1.290) = 0.9015. So what would be the probability you want, P(z > 1.290)?
rexxii said:
Said the breaking load is 90.15%

I know this is incorrect please can you advise The probability that a randomly selected cable will have a breaking load greater breaking load than 6200 Newtons is 90%.
 
  • #3
So i need to read from the RHS side? as it is above the mean? Would i still select that number or a different one of the table?
 
  • #4
P(z < 1.290) = .9015, from the table. The number .9015 represents the area under the standard normal curve between ##z = -\infty## and z = 1.290. What is the total area under the curve? What's the area under the curve between z = 1.290 and ##z = +\infty##?
 
  • #5
1.29 - 1 = 0.29 above the mean?
 
  • #6
rexxii said:
1.29 - 1 = 0.29 above the mean?
No, and this doesn't make any sense -- you're mixing two unrelated things there: the z-value and the probability associated with a certain z-value.

Have you seen a graph of the standard normal curve? In the standard normal distribution, half of the area under the curve is to the left of the mean at z = 0, and the other half is to the right. What's the total area under the curve? How much of the area under the curve lies to the left of z = 1.29? How much of the area lies to the right of z = 1.29?

It would be a good idea to read the section in your textbook that has this problem. There's quite a bit you don't understand.
 

1. What is the probability of a cable having a breaking load greater than 6200 N?

The probability of a cable having a breaking load greater than 6200 N depends on several factors, such as the material, diameter, and manufacturing process of the cable. It is not possible to accurately determine the probability without specific information about the cable in question.

2. Can you calculate the probability based on the strength of the cable material?

The strength of the cable material is one of the factors that can influence the probability of a cable having a breaking load greater than 6200 N. However, other factors such as the diameter and manufacturing process also play a significant role in determining the probability. Therefore, it is not possible to accurately calculate the probability based solely on the strength of the cable material.

3. How does the diameter of the cable affect the probability?

The diameter of the cable is an important factor in determining the probability of it having a breaking load greater than 6200 N. Generally, a thicker cable has a higher probability of withstanding a greater load. However, other factors such as the material and manufacturing process also play a role in determining the probability.

4. Is there a standard or average probability for cables to have a breaking load greater than 6200 N?

There is no standard or average probability for cables to have a breaking load greater than 6200 N. The probability varies depending on the specific characteristics and quality of the cable. It is important to note that cables are designed to withstand certain loads, and exceeding the breaking load can lead to failure and potential safety hazards.

5. Can the probability be increased by using a specific manufacturing process?

The manufacturing process can influence the probability of a cable having a breaking load greater than 6200 N. For example, a cable made using high-quality materials and precise manufacturing techniques may have a higher probability of withstanding a greater load. However, other factors such as the diameter and design of the cable also play a role in determining the probability, so it cannot be solely attributed to the manufacturing process.

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