In a sample of 80 light bulbs, the mean lifetime was 1217 hours with a standard deviation of 52 hours. a. Find the 95% confidence interval for the mean lifetime of this type of bulb. Justify the reason you chose the distribution used to construct the confidence interval. b. How many light bulbs must be sampled so that a 95% confidence interval will specify the mean lifetime to within + 8 hours?
Complete Question
In a sample of 80 light bulbs, the mean lifetime was 1217 hours with a standard deviation of 52 hours. a. Find the 95% confidence interval for the mean lifetime of this type of bulb. Justify the reason you chose the distribution used to construct the confidence interval. b. How many light bulbs must be sampled so that a 95% confidence interval will specify the mean lifetime to within [tex]\pm 8 \ hours[/tex]?
Answer:
a
[tex]1206 < \mu < 1228 [/tex]
The reason why a normal distribution was chosen is because the sample size is large enough that is [tex]n > 30[/tex]
b
[tex]n =162 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 80
The sample mean is [tex]\= x = 1217[/tex]
The standard deviation is [tex]\sigma = 52[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{ 52}{\sqrt{80} }[/tex]
=> [tex]E = 11.395 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex]1217 -11.395 < \mu < 1217 + 11.395[/tex]
=> [tex]1206 < \mu < 1228 [/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ] ^2[/tex]
Here E = 8
=> [tex]n = [\frac{1.96 * 52 }{8} ] ^2[/tex]
=> [tex]n =162 [/tex]
Find the GCF of 32, 64, and 96. The GCF is _______.
Answer:
128
Step-by-step explanation:
If you multiply you get it.
Answer:
The GCF of these numbers are 32.
Step-by-step explanation:
All of these integers are able to be divided, and by the first number.
Hope this helps! :3
What is the value of 3-(-2)? 25 -3 -2 -1 0 1 5 0 1 O 5
Answer:
5
Step-by-step explanation:
(because when two negative meets it gives u positive )
Answer this question please and i will give brainliest
Answer:
false the answer is false
Step-by-step explanation:
(Angle relationships) solve this question.
Answer:
21
Step-by-step explanation:
Old Navy is having a sale for the summer they are selling for shirts for $23 what is the price per share at the store
Answer:
5 dollars and 75 cents.
Step-by-step explanation:
I think you mean 4 shirts are 23$? If so ,you would divide 23 by 4 to get how many dollars is 1 shirt. 23/4 = 5.75
PLZ HURRY IT'S URGENT!!
Which equation matches the scenario?
Maggie has $15 to spend. Pinball games cost $0.75 per play and skee-ball games cost $1.25 per play.
Question 4 options:
A. 15x+0.75y≤1.25
B. 0.75x+1.25y≤15
C. (0.75+1.25)x<15
D. 0.75x+1.25y≥15
Answer:
B. 0.75x + 1.25y [tex]\leq[/tex] 15
what’s this answer please need help
Answer: -1 [(y-b)/m]+x=a
Step-by-step explanation:
(Y-b) / m = x-a
[(y-b)/m] -x =-a
-1 [(y-b)/m]+x=a
Figure ABCD is a parallelogram.
Parallelogram A B C D is shown. The length of A B is 3 y minus 2, the length of B C is x + 12, the length of D C is y + 6, and the length of A D is 2 x minus 4.
What are the lengths of line segments AB and BC?
AB = 4; BC = 16
AB = 4; BC = 8
AB = 10; BC = 20
AB = 10; BC = 28
The lengths of line segments AB and BC are AB = 10; BC = 28
What are parallelograms?Parallelograms are shapes with parallel and equal opposite sides
The given parameters are:
AB = 3y - 2
BC = x + 12
DC = y + 6
AD = 2x - 4
The above means that:
AB = DC
BC = AD
So, we have:
AB = DC
3y -2 = y + 6
Collect like terms
3y - y = 2 + 6
2y = 8
Divide by 2
y = 4
Also, we have:
BC = AD
x + 12 = 2x - 4
Collect like terms
2x - x = 4 + 12
x = 16
The lengths AB and BC are given as:
AB = 3y - 2
BC = x + 12
So, we have:
AB = 3*4 - 2
AB = 10
BC = x + 12
BC =16 + 12
BC = 28
Hence, the lengths of line segments AB and BC are AB = 10; BC = 28
Read more about parallelograms at:
https://brainly.com/question/24056495
Answer:
D
Step-by-step explanation:
I don’t get this question at all, pls help. I just need the function.
subtracting decimals
0.89-0.6
Answer:
o.29 answer of this question
Answer:
0.29
Step-by-step explanation:
0 . 8 9
-0 . 6 0
-------------
0 . 2 9
--------------
Hope this helps
plz mark as brainliest!!!!!!!!
I WILL MARK BRAINLIST
Answer:
The answer would be c
Step-by-step explanation:
If you look at the vertices you will see that none of them have any of the same vertices.
Type the following fractions in order from greatest to least:
5/4, 4/10, 5/12, ¼, 11/12
Write the decimals in the boxes from greatest to least:
0.5, 0.91, 0.04, 0.89, 0.51
Answer:
5/4, 11/12, 1/4, 5/12, 4/10 0.91, 0.89, 0.51, 0.5, 0.04
Step-by-step explanation:
Im pretty sure these are correct
Compare. Select <, >, or=.
6.61? 6.610
The awnser is 6.610
Answer:
6.61=6.610
Step-by-step explanation:
6.61=6.610
After point we can increase no. Of zero.
Callista used 10% off coupon to purchase a band t-shirt from Hot Topic . If the shirt cost $21.00, what is the discount in dollars?
Answer:
The discount is 2.1 dollars
answer fast and quickly plsss
Answer:
C. 65°, 115°
Step-by-step explanation:
3x - 5 + 2x - 15 = 180
5x - 20 = 180
5x = 180 + 20
5x = 200
x = 200/5
x = 40
5x - 20 = 3*40-5 = 120 - 5 = 115
2x - 15 = 2*40 - 15 = 80 - 15 = 65
Given f(x) = 2x2 + 4x - 3 and g(x) = 5x - 2, find f(x) - g(x).
Must show all work to receive credit! Show your work in the box below
Answer:
its the same steps as the other one I answered for you except subtract
Step-by-step explanation:
x-1
Answer:
f(x) - g(x) = 2x^2 - x - 1
Step-by-step explanation:
f(x) = 2x^2 + 4x - 3 g(x) = 5x - 2
f(x) - g(x) = (2x^2 + 4x - 3) - (5x - 2)
= 2x^2 + 4x - 3 - 5x + 2
= 2x^2 - x - 1
A tailor charge $560 for a suit of clothes and gives a discount of 12% for cash. Calculate the discounted price for a suit of clothes.
Answer:
$492.80
Step-by-step explanation:
The discount= 12%*$560/100%
= $67.20
The discounted= Selling price- discount
= $560 - $67.20
= $492.80
Use a half-angle identity to find the exact value of sin 3pi/8
The above answer is correct! The correct response is A.
Just got it right on edge 2020, hope this helps!! Good luck, and have a great day! :)
The solution is, Using a half-angle identity we get the exact value of
sin 3pi/8 is ±√[(2 + √2) / 4].
Here, we have,
The half angle formula of sin in trigonometry is
sin A/2 = ±√[(1 - cos A) / 2].
If 0 < x < π/2 , then cos x > 0.
now, we have,
sin 3pi/8
here, A/2 = 3pi/8 so, A = 3pi/4 = 6π/8
applying this half angle formula of sin in trigonometry
we get,
sin 3π/8 = ±√[(1 - cos 6π/8) / 2]
= ±√[(1 + 1/√2) / 2]
= ±√[(2 + √2) / 4]
so, we get,
sin 3π/8 = ±√[(2 + √2) / 4]
Hence, The solution is, Using a half-angle identity we get the exact value of sin 3pi/8 is ±√[(2 + √2) / 4].
For more such question on sin in trigonometry visit:
brainly.com/question/26098092
#SPJ6
Select all angles of symmetry.
Answer:
B,C,F
Step-by-step explanation:
Which of the following correctly identifies the set of outputs?
{(5, –2), (1, –1), (–2, 2), (2, 5)}
{(–2, 5), (–1, 1), (2, –2), (5, 2)}
{–2, –1, 2, 5}
{–2, 1, 2, 5}
There are 19.3 cups of flour in a bag. The chef uses 2.9 cups for making cookies.
Then, he uses 1.2 cups of sugar and 5.1 cups of flour for making banana bread.
How many cups of flour are left?
Answer:
10.1 cups left
Hope this helps!
Can you pls give brainly if this helps
Which of these statements is true about adaptive evolution?
Answer:
Adaptive evolution is always changing because the environment is changing continuously.
Hence,
The right answer would be :
Adaptive evolution is a fluctuating change in a trait
Step-by-step explanation:
PLZ I WILL GIVE BRAINLEST
Bobby has 38 dolar and his siter had 92 dolar how much more money sister have?
Answer:
54
Step-by-step explanation:
92 (how much his sister has) - 38 (how much he has) = 54 (how much more money his sister has then him)
Answer: His sister had 54 more dollars than him.
Step-by-step explanation: 92 (sister's amount) -38 (Bobby's amount) = 54 (total difference).
Please help with the problem in the picture ^ I’ll give brainliest if you give me a small explanation! :)
Answer:
x=16 because the proportional size, this also means that if the -84 becomes 16 in proportion size.
In a random sample of 500 college students, 23% say that they read or watch the news every day. Develop a 90% confidence interval for the proportion of all students who read or watch the news on a daily basis. Interpret your results. If you wanted to develop a 95% confidence interval with a margin of error of .01, how many students would need to be surveyed?
Answer:
The 90% confidence interval is [tex]0.199 < p < 0.261 [/tex]
The sample size to develop a 95% confidence interval is [tex]n = 2032 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n =500
The sample proportion is [tex]\^ p = 0.23[/tex]
From the question we are told the confidence level is 90% , hence the level of significance is
[tex]\alpha = (100 - 90 ) \%[/tex]
=> [tex]\alpha = 0.10[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } [/tex]
=> [tex]E = 1.645 * \sqrt{\frac{0.23 (1- 0.23)}{500} } [/tex]
=> [tex]E = 0.03096 [/tex]
Generally 90% confidence interval is mathematically represented as
[tex]\^ p -E < p < \^ p +E[/tex]
=> [tex]0.23 -0.03096 < p < 0.23 + 0.03096 [/tex]
=> [tex]0.199 < p < 0.261 [/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
The margin of error is given as [tex]E = 0.01[/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) [/tex]
=> [tex]n = [\frac{1.96 }{0.01} ]^2 *0.23 (1 - 0.23 ) [/tex]
=> [tex]n = 2032 [/tex]
which is a unit rate?
A. 15 miles per gallon
B. 5 pounds in two bags
C. $8 for three boxes of crackers
D. 22 gallons in 5 days
help pls this is due today:(
Answer:
5cm
Step-by-step explanation:
a^2+b^2=c^2
9+16=x^2
25=x^2
x=5
Hope this helps!
4x + 11y = 7
4x + 3y = -1
Answer:
x= - 1
y= 1
Step-by-step explanation:
qwertyuiopsknzvzbjzjjs
Today Angela's cat's age in months is the same as Angela's age in years. In one year her cat's age in months will be 2 times Angela's age in years. Today Angela is ___years old.
Answer:
10
Step-by-step explanation:
I just guessed and check :)
But if you recheck my answer it's correct!
Angela: 10 years
Cat: 10 months
In 1 year:
Angela: 11 years
Cat: 22 months
I hope this helps!
Answer:
I think Angela is 10 years old today.