1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
PilotLPTM [1.2K]
3 years ago
15

Cable Strength: A group of engineers developed a new design for a steel cable. They need to estimate the amount of weight the ca

ble can hold. The weight limit will be reported on cable packaging. The engineers take a random sample of 45 cables and apply weights to each of them until they break. The mean breaking weight for the 45 cables is 768.2 lb. The standard deviation of the breaking weight for the sample is 15.1 lb. Using the sample information as given, construct a confidence interval for the mean breaking strength of the new steel cable.
Mathematics
1 answer:
KatRina [158]3 years ago
3 0

Answer:

95% confidence interval for the mean breaking strength of the new steel cable is [763.65 lb , 772.75 lb].

Step-by-step explanation:

We are given that the engineers take a random sample of 45 cables and apply weights to each of them until they break. The mean breaking weight for the 45 cables is 768.2 lb. The standard deviation of the breaking weight for the sample is 15.1 lb.

Since, in the question it is not specified that how much confidence interval has be constructed; so we assume to be constructing of 95% confidence interval.

Firstly, the Pivotal quantity for 95% confidence interval for the population mean is given by;

                            P.Q. =  \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample mean breaking weight = 768.2 lb

            s = sample standard deviation = 15.1 lb

            n = sample of cables = 45

            \mu = population mean breaking strength

Here for constructing 95% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.

<u>So, 95% confidence interval for the population mean, </u>\mu<u> is ;</u>

P(-2.02 < t_4_4 < 2.02) = 0.95  {As the critical value of t at 44 degree

                                           of freedom are -2.02 & 2.02 with P = 2.5%}  

P(-2.02 < \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } } < 2.02) = 0.95

P( -2.02 \times {\frac{s}{\sqrt{n} } } < {\bar X-\mu} < 2.02 \times {\frac{s}{\sqrt{n} } } ) = 0.95

P( \bar X-2.02 \times {\frac{s}{\sqrt{n} } } < \mu < \bar X+2.02 \times {\frac{s}{\sqrt{n} } } ) = 0.95

<u>95% confidence interval for</u> \mu = [ \bar X-2.02 \times {\frac{s}{\sqrt{n} } } , \bar X+2.02 \times {\frac{s}{\sqrt{n} } } ]

                                     = [ 768.2-2.02 \times {\frac{15.1}{\sqrt{45} } } , 768.2+2.02 \times {\frac{15.1}{\sqrt{45} } } ]

                                     = [763.65 lb , 772.75 lb]

Therefore, 95% confidence interval for the mean breaking strength of the new steel cable is [763.65 lb , 772.75 lb].

You might be interested in
Four rulers and three pencils cost £2.15
Lubov Fominskaja [6]

Answer:

4r + 3p = 2.15

3r + 4p = 2.05

I have no idea.......

4 0
3 years ago
I need help on this final problem​
bulgar [2K]

Answer:

1/2 (1 - 10 d)

Hope This Helps & Good Luck ^^

8 0
3 years ago
Find the quotient.<br><br> 35.4 ÷ 0.59
AleksandrR [38]

Answer:

35.4÷ 0.59=60

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Stan has listened to 1/3 of his favorite CD. His favorite CD has 12 songs. How many songs has he
alekssr [168]
4, one third of 12 is 4
4 0
3 years ago
Read 2 more answers
4x+x+6=11x-6x+6 what is the value for x
sveticcg [70]

Answer:

use papamath it will give u the anwers

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • can someone do my ixl its 6th grade math!! only 3 and you have to get 85 and higher i will give 25 points!! and mark as brainlis
    5·2 answers
  • How to change a quadratic equation into intercept form?
    6·1 answer
  • Determine the intercepts of the line. − 6 x + 3 y = − 7
    8·1 answer
  • What is the exact value of cos 22.5°?
    6·1 answer
  • Starting with 2 marked points, A and B, precisely describe the straightedge and compass moves required to construct the triangle
    6·1 answer
  • I am having trouble with these equations <br> 7x + 2y = - 8<br> 8y = 4x<br> solve using substitution
    11·1 answer
  • Pls help <br> Thank you for your cooperation &lt;3
    5·2 answers
  • B=<br> Round your answer to the nearest hundredth.<br> с<br> B<br> ?<br> 2<br> 9<br> А
    9·1 answer
  • What is the decrease percentage of 62 to 31
    5·2 answers
  • What are sides 'a' and 'b' called in a right triangle
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!