Question

In: Statistics and Probability

A certain type of cable has a mean breaking point of 159 pounds with a standard...

A certain type of cable has a mean breaking point of 159 pounds with a standard deviation of 6 pounds. What weight should be specified so that 95​% of the cables can be expected not to break supporting that​ weight?

Solutions

Expert Solution

Answer:

Given that:

A certain type of cable has a mean breaking point of 159 pounds with a standard deviation of 6 pounds.

Mean () = 159

Standard deviation ()=6

The z-score is 3.33 for top 95% that is for A=0.500

For a normal distribution with mean and standard deviation the size is

Here x is the non standard distribution to a z-score

To find the cutoff for an F,plug in , z-score in the above formula and solve for x

So

Therefore,the cutoff of breaking point of a certain type of cable in the top 95% is 179 pounds

orchestra answered 2 years ago
Next > < Previous

Related Solutions

A special cable has breaking strength of 800 pounds. the standard deviation of the population is...
A special cable has breaking strength of 800 pounds. the standard deviation of the population is 12 pounds . A research selects a sample of 20 cables and finds that the average breaking strength is 793 pounds. test the claim that breaking strength is less than 800 pounds. Should the null hypothesis be rejected at a=0.01? Assuming that the variable is normally distributed.
I need explanation for this problem: The breaking strength of a certain type of fabric has...
I need explanation for this problem: The breaking strength of a certain type of fabric has mean 1.86 and standard deviation .2. A random sample of 49 pieces of fabric is drawn. A- What is the probability that the sample mean breaking strength is less than 1.8? B- How large a sample size is needed so that the probability is .06 that the sample mean is less than 1.8? Ans for (A)= 0.02 Ans for (B)= 27
The breaking strength X of a certain rivet used in a machine engine has a mean...
The breaking strength X of a certain rivet used in a machine engine has a mean 5000 psi and standard deviation 400 psi. A random sample of 25 rivets is taken. Consider the distribution of ?̅, the sample mean breaking strength. (a) What is the probability that the sample mean falls between 4800 psi and 5200 psi? (b) What sample n would be necessary in order to have P(4950 < ?̅<5050) = 0.95 (0.99)?
The mean and standard deviation for the diameter of a certain type of steel rod are...
The mean and standard deviation for the diameter of a certain type of steel rod are mu = 0.503 cm and sigma = 0.03cm. Let X denote the average of the diameters of a batch of 100 such steel rods. The batch passes inspection if Xbar falls between 0.495 and 0.505cm. 1. What is the approximate distribution of Xbar? Specify the mean and the variance and cite the appropriate theorem to justify your answer. 2. What is the approximate probability...
Given an approximately normal distribution with a mean of 159 and a standard deviation of 17,...
Given an approximately normal distribution with a mean of 159 and a standard deviation of 17, a) Draw a normal curve and label 1, 2, and 3 standard deviations on both sides on the mean. b) What percent of values are within the interval (142, 176)? c) What percent of values are within the interval (125, 193)? d) What interval contains 99.7% of all values? e) What percent of values are above 176? f) What percent of values are below...
In an experiment involving the breaking strength of a certain type of thread used in personal...
In an experiment involving the breaking strength of a certain type of thread used in personal flotation devices, one batch of thread was subjected to a heat treatment for 60 seconds and another batch was treated for 120 seconds. The breaking strengths (in N) of ten threads in each batch were measured. The results were 60 seconds: 43 52 52 58 49 52 41 52 56 58 120 seconds: 59 55 59 66 62 55 57 66 66 51 Let...
In an experiment involving the breaking strength of a certain type of thread used in personal...
In an experiment involving the breaking strength of a certain type of thread used in personal flotation devices, one batch of thread was subjected to a heat treatment for 60 seconds and another batch was treated for 120 seconds. The breaking strengths (in N) of ten threads in each batch were measured. The results were 60 seconds: 43 52 52 58 49 52 41 52 56 50 120 seconds: 59 55 59 66 62 55 57 66 66 51 Let...
In an experiment involving the breaking strength of a certain type of thread used in personal...
In an experiment involving the breaking strength of a certain type of thread used in personal flotation devices, one batch of thread was subjected to a heat treatment for 60 seconds and another batch was treated for 120 seconds. The breaking strengths (in N) of ten threads in each batch were measured. The results were 60 seconds:     43    52    52    58    49    52    41    52    56    58 120 seconds:   59    55    59    66    62    55    57    66    66    51 Let...
The specifications for a certain kind of ribbon call for a mean breaking strength of 185...
The specifications for a certain kind of ribbon call for a mean breaking strength of 185 pounds. Suppose five pieces are randomly selected from different rolls. The breaking strengths of these ribbons are 171.6, 191.8, 178.3, 184.9 and 189.1 pounds. You are required to perform an appropriate hypothesis test by formulating the null hypothesis µ = 185 against the alternative hypothesis test µ < 185 at α = 0.10. (i) What is the critical region for the test? (ii) What...
The breaking strengths of cables produced by a certain manufacturer have a mean, μ , of...
The breaking strengths of cables produced by a certain manufacturer have a mean, μ , of 1900 pounds, and a standard deviation of 100 pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, 21 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1959 pounds. Assume that the population is normally distributed. Can we support, at the 0.1 level of...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT