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
AURORKA [14]
3 years ago
7

On the basis of extensive tests, the yield point of a particular type of mild steel-reinforcing bar is known to be normally dist

ributed with σ = 100. The composition of the bar has been slightly modified, but the modification is not believed to have affected either the normality or the value of σ. 94
Mathematics
1 answer:
Fofino [41]3 years ago
7 0

Answer:

a) 8469-1.645\frac{100}{\sqrt{64}}=8448.4    

8469+1.645\frac{100}{\sqrt{64}}=8489.6    

So on this case the 90% confidence interval would be given by (8448.4;8489.6)    

b) 8469-2.054\frac{100}{\sqrt{64}}=8443.33    

8469+2.054\frac{100}{\sqrt{64}}=8494.68    

So on this case the 96% confidence interval would be given by (8443.33;8494.68)    

Step-by-step explanation:

Assuming this complete problem: On the basis of extensive tests, the yield point of a particular type of mild steel-reinforcing bar is known to be normally distributed with s = 100. The composition of the bar has been slightly modified, but the modification is not believed to have affected either the normality or the value of s.

(a) Assuming this to be the case, if a sample of 64 modified bars resulted in a sample average yield point of 8469 lb, compute a 90% CI for the true average yield point of the modified bar. (Round your answers to one decimal place.)

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X=8469 represent the sample mean

\mu population mean (variable of interest)

\sigma=100 represent the population standard deviation

n=64 represent the sample size  

The confidence interval for the mean is given by the following formula:

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)

Since the Confidence is 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.05, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that z_{\alpha/2}=1.645

Now we have everything in order to replace into formula (1):

8469-1.645\frac{100}{\sqrt{64}}=8448.4    

8469+1.645\frac{100}{\sqrt{64}}=8489.6    

So on this case the 90% confidence interval would be given by (8448.4;8489.6)    

(b) How would you modify the interval in part (a) to obtain a confidence level of 96%? (Round your answer to two decimal places.)

Since the Confidence is 0.96 or 96%, the value of \alpha=0.04 and \alpha/2 =0.02, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.02,0,1)".And we see that z_{\alpha/2}=2.054

Now we have everything in order to replace into formula (1):

8469-2.054\frac{100}{\sqrt{64}}=8443.33    

8469+2.054\frac{100}{\sqrt{64}}=8494.68    

So on this case the 96% confidence interval would be given by (8443.33;8494.68)    

You might be interested in
Solve [3(4-1)-7] - [6-(4-9)]
d1i1m1o1n [39]

Answer:

-9

Step-by-step explanation:

7 0
3 years ago
(10 points/I really need help) Tomas needs exactly 6 potatoes to make 12 potato pancakes?? Which of the following statements are
kirill115 [55]

The answers are A, B, and D.

The given information is that Tomas needs 6 potatoes to make 12 potato pancakes. Thus, we can assume it takes 1 potato to make 2 potato pancakes.

An answer choice must have two times more pancakes than potatoes. Only A, B, and D satisfy this. The others can be confusing if the multiplication is not executed properly.

3 0
3 years ago
Read 2 more answers
Please help me with this please and thank you
Bond [772]
I can’t see the problem very well, but your answer should be the one with (-3/2,0) as the intersecting point on the graph.
5 0
2 years ago
Express number 9 as a unit rate, you can also round
Katena32 [7]
125/200= 0.625 cents

0.625 cents to the nearest cent= 0.63

The unit rate is 0.63 miles.

Hope this helps!







6 0
3 years ago
On your cell phone bill, you are charged $0.25 for each text you send. What is the dependent variable?
zhannawk [14.2K]

Answer:

The amount of the bill is dependent on the number of texts sent. Let y be the bill amount and x the number of texts. Then x is independent and y is dependent. This is because x can be any non-negative number, but y depends upon it. You cannot find the bill without knowing the number of text messages, right?

3 0
3 years ago
Read 2 more answers
Other questions:
  • Can u help me ok the first one plz
    5·1 answer
  • An economy package of cups has 500 green cups if the green cups are 20% of the total package how many cups are in the package
    15·1 answer
  • Need help here guys.
    13·1 answer
  • Factorise the following expressions m²-9n²​
    13·1 answer
  • Which of the following theorems verified that angle xyz is congruent too angle uwv?
    9·1 answer
  • The product of a number m and 6 is no less than 30.
    8·2 answers
  • I need help asap :(​
    7·1 answer
  • A deep freezer has a temperature of -6°C when it is turned off.
    12·1 answer
  • Answer this please....
    10·1 answer
  • Please help me! will mark brainliest
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!