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
KatRina [158]
3 years ago
10

Question 1.05 It is known from past experience that the life of traffic light bulbs is normally distributed with a standard devi

ation of 250 hours. In a study, if you wanted the total width of the two-sided confidence interval on mean to be 120 hours at 90% confidence, how many light bulbs should be selected for the study
Mathematics
2 answers:
Olenka [21]3 years ago
5 0

Answer:

n=(\frac{1.64(250)}{60})^2 =46.69 \approx 47

So the answer for this case would be n=47 rounded up to the nearest integer

Step-by-step explanation:

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 represent the sample mean for the sample  

\mu population mean (variable of interest)

\sigma= 250 represent the population standard deviation

n represent the sample size  

Solution to the problem

For this case the width of the interval is 120 and we have the following relation:

ME = \frac{width}{2}= \frac{120}{2}=60

The margin of error is given by this formula:

ME=z_{\alpha/2}\frac{s}{\sqrt{n}}    (a)

And on this case we have that ME =60 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2   (b)

The critical value for 90% of confidence interval now can be founded using the normal distribution. And in excel we can use this formula to find it:"=-NORM.INV(0.05;0;1)", and we got z_{\alpha/2}=1.64, replacing into formula (b) we got:

n=(\frac{1.64(250)}{60})^2 =46.69 \approx 47

So the answer for this case would be n=47 rounded up to the nearest integer

dimulka [17.4K]3 years ago
3 0

Answer:

The required sample size of lightbulbs = 47

Step-by-step explanation:

The total width of the two-sided confidence interval on mean to be 120 hours at 90% confidence.

That is, 60 hours on top and below the mean.

Confidence interval = (Sample mean) ± (Margin of error)

So, from this description that the interval is of width 120 hours of the mean and 60 hours, below and above the mean,

Margin of error = 60 hours.

Margin of Error = (critical value) × (standard deviation of the distribution of sample means)

Critical value for 90% confidence = 1.645

Standard deviation of the distribution of sample means = (standard deviation) ÷ √n

where n = sample size = ?

Standard deviation = 250 hours

60 = 1.645 × (250/√n)

√n = (1.645×250)/60 = 6.854

n = 6.854² = 46.98 = 47 (approximated to the closest whole number)

Hope this Helps!!!

You might be interested in
Use the function below to find F(3)
garik1379 [7]

Answer:

Theanswer is 4/27.

Step-by-step explanation:

given that, F(x) = 4×(1/3)^x

now , F(3)= 4×(1/3)^3 ( putting value of x)

or, F(3) = 4×(1/27)

therefore, F(3)= 4/27... ans

<em><u>hope</u></em><em><u> </u></em><em><u>it helps</u></em><em><u>.</u></em><em><u>.</u></em>

8 0
3 years ago
Pls helpppp me I’m super stuckkk
weeeeeb [17]

Answer:

slope=2

Step-by-step explanation:

subrtract -4-(-4) the two negatives make it a + so that becomes 8 and thats for the top one the bottom is 6-2 which is 4 then divide 8 by 4 to find the slope which is 2.

5 0
3 years ago
Which equation and solution can be used to solve this problem?
maks197457 [2]

Answer:

D

Step-by-step explanation:

We need to convert these words into mathematical expressions:

- "Twenty-two less than a number"; "less than" indicates that we need to use subtraction, and since it's "twenty-two less than", we have: -22. Let's say the "number" is q. Then, we have -22 of q, which is q - 22.

- "is twenty-four"; "is" in math always means "equal", so we need an equal sign with 24 next to it: = 24

Put this altogether:

q - 22 = 24

The answer is thus D.

4 0
3 years ago
Read 2 more answers
What are the next three terms of the following sequence?
kaheart [24]

we know that given terms were i geometric progression.

which means common ratio is same between two consecutive terms .

here we have 8,40,200,1000.

we know that common ratio =second term/first term =40/8=5.

so each and every terms is multiplied by 5 to get next term for this series the term after 1000 is 5000 =1000*5.

in part b we have another series which is having common ratio of -2.

so we need to multiply with -2 to find next term.

80*(-2)=-160.

for part c the common ratio is -2 .

so we need to multiply with -2 *previous term =-2*16 =-32.

5 0
3 years ago
Read 2 more answers
What is the side length of a cube with a volume of 2197 cm3?
Nataliya [291]
The side length of a cube would be the cube root of its volume, because it's length, width and height are all the same. So the answer is 13
7 0
2 years ago
Other questions:
  • Pleas help I’m in a hurry
    11·1 answer
  • The following function represents the profit P(n), in dollars, that a concert promoter makes by selling tickets for n dollars ea
    7·1 answer
  • Using the graph as your guide, complete the following statement.
    5·1 answer
  • Two functions are graphed on the coordinate plane.
    11·1 answer
  • The length of a rectangle is given by x + 2 and its width is equal to 3. Give a simplified expression of the area of this rectan
    14·2 answers
  • GIVING BRAINLIST TO WHOEVER ANSWERS
    5·1 answer
  • PLEASE HELP I GIVE BRAINLIST! THIS IS ALMOST DUE!
    14·1 answer
  • Find the value of the following expression using a number line.<br><br> 3+(−2)
    8·2 answers
  • Please guys solve Ex:4 ,i don't know it​
    5·2 answers
  • Find an expression which represents the difference when (9x−6) is subtracted from (6x+7) in simplest terms.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!