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
erma4kov [3.2K]
3 years ago
5

Refrigerators in a random sample of 60 refrigerators, the mean repair cost was $150.00 and the standard deviation was $15.50. Co

nstruct a 99% confidence interval for the population mean repair cost. Interpret the results.
Mathematics
1 answer:
worty [1.4K]3 years ago
7 0

Answer:

The 99% confidence interval is given by ($144.677;$155.323)  

We are confidenct at 99% that the true mean for the reapir cost of refrigerators is between 144.677 and 155.323.

Step-by-step explanation:

1) Notation and definitions  

n=60 represent the sample size  

\bar X= 150 represent the sample mean  

s=15.5 represent the sample standard deviation  

m represent the margin of error  

Confidence =99% or 0.99

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".  

2) Calculate the critical value tc  

In order to find the critical value is important to mention that we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 99% of confidence, our significance level would be given by \alpha=1-0.99=0.01 and \alpha/2 =0.005. The degrees of freedom are given by:  

df=n-1=60-1=59  

We can find the critical values in excel using the following formulas:  

"=T.INV(0.005,59)" for t_{\alpha/2}=-2.66  

"=T.INV(1-0.005,59)" for t_{1-\alpha/2}=2.66  

The critical value tc=\pm 2.66  

3) Calculate the margin of error (m)  

The margin of error for the sample mean is given by this formula:  

m=t_c \frac{s}{\sqrt{n}}  

m=2.66 \frac{15.5}{\sqrt{60}}=5.323  

4) Calculate the confidence interval  

The interval for the mean is given by this formula:  

\bar X \pm t_{c} \frac{s}{\sqrt{n}}  

And calculating the limits we got:  

150 - 2.66 \frac{15.5}{\sqrt{60}}=144.677  

150 + 2.66 \frac{15.5}{\sqrt{60}}=155.323  

The 99% confidence interval is given by ($144.677;$155.323)  

We are confidenct at 99% that the true mean for the reapir cost of refrigerators is between 144.677 and 155.323.

You might be interested in
What is a point-slope equation of the line with slope -10 that goes through the point (1,4)?
Svet_ta [14]

Answer:

<h3>The answer is option A</h3>

Step-by-step explanation:

To find an equation of a line in point slope form when given the slope and a point we use the formula

y -  y_1 = m(x -  x_1)

where

m is the slope

( x1 , y1) is the point

From the question

the slope is - 10

the point is (1,4)

So the equation of the line is

<h2>y - 4 =  - 10(x - 1)</h2>

Hope this helps you

8 0
2 years ago
Leon is building a square picture frame. The side of the frame is 495 millimeters long. If a meter of wood costs $7, how much wi
REY [17]

Answer:

3.465

Step-by-step explanation:

Also can you give brainliest to all of your questions bc it really hard to get brainliest and it be really nice you can choose who i dont really care but just please do it it helps a lot

3 0
3 years ago
You borrowed 43,800 at a SIMPLE interest rate of 4.8%. If you pay it back in 2 years, how much
Naddik [55]

Answer:

I = $4204.8

Step-by-step explanation:

Given that,

Principal, P = $43,800

Interest rate = 4.8%

Rate = 2 years

We need to find the interest that is paid back. We know that, simple interest is given by :

I=\dfrac{PRT}{100}

Put all the values,

I=\dfrac{43800\times 4.8\times 2}{100}\\\\=\$4204.8

So, the required interest is equal to $4204.8 .

3 0
2 years ago
Add: f(x)+g(x)<br> f(x) = 2x2 – 3x² + 7x+1<br> g(x) = 4x2 + 5x +12<br> Submit
prisoha [69]

Answer:

f(x) + g(x) = 2x^3 + x^2 + 12x + 13

Step-by-step explanation:

We are given these following functions:

f(x) = 2x^3 - 3x^2 + 7x + 1

g(x) = 4x^2 + 5x + 12

Add: f(x)+g(x)

To add them, we combine the like terms. So

f(x) + g(x) = 2x^3 - 3x^2 + 7x + 1 + 4x^2 + 5x + 12 = 2x^3 + (-3+4)x^2 + (7+5)x + 1 + 12 = 2x^3 + x^2 + 12x + 13

The added function is:

f(x) + g(x) = 2x^3 + x^2 + 12x + 13

8 0
2 years ago
Yesterday, Jake rode his bike 6.6 miles. Today he rode2.4 times as far, how many miles did he ride today?
Paul [167]

Answer:

15.84

Step-by-step explanation:

6.6 × 2.4 = 15.84

he rode 15.84 miles today

3 0
3 years ago
Other questions:
  • How are equivalent fractions used in renaming when subtracting?
    14·1 answer
  • What is the common difference for this arithmetic sequence?
    8·2 answers
  • A study found that 9% of dog owners brush their dog’s teeth. Of 578 dog owners, about how many would be expected to brush their
    11·1 answer
  • The sum of the numbers as the product of their GCF and other sum so what is 32 plus 20???
    12·1 answer
  • The vertex form of the equation of a parabola is y = 4(x - 2)2 - 1.What is the standard form of the equation?
    9·1 answer
  • Count by 5 135 to 175 describe the pattern
    6·1 answer
  • Write an equation in slope-intercept form of the line that passes through (-1,4) and (0,2).
    11·2 answers
  • 3.
    7·2 answers
  • PLEASE HELP MEeeeeee D:
    14·2 answers
  • How many groups of 6 are in 95?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!