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
ICE Princess25 [194]
3 years ago
11

The company states that 90% of the light bulbs have a lifetime of at least k hours. Find the value of k. Give your answer correc

t to the nearest hundred.​

Mathematics
1 answer:
docker41 [41]3 years ago
5 0

Answer:

a) Mean = 5800 hours

b) P(5000 ≤ L ≤ 6000) = 0.420

c) k = 4700 hours

Step-by-step explanation:

The full correct question is attached to this solution.

From the graph of the distribution of lifetime of bulbs presented, it is evident that this is a normal distribution.

(a) Write down the mean lifetime of the light bulbs.

From the normal distribution graph, the mean is at the very centre of the graph

Mean = μ = 5800 hours

(b) The standard deviation of the lifetime of the light bulbs is 850 hours.

Find the probability that 5000 ≤ L ≤ 6000, for a randomly chosen light bulb.

Mean = μ = 5800 hours

Standard deviation = σ = 850 hours.

The required probability = P(5000 ≤ L ≤ 6000)

To find this, we first normalize/standardize 5000 and 6000.

The standardized score for any value is the value minus the mean then divided by the standard deviation.

For 5000

z = (L- μ)/σ = (5000 - 5800)/850 = -0.941

For 6000

z = (L- μ)/σ = (6000 - 5800)/850 = 0.235

The required probability

P(5000 ≤ L ≤ 6000) = P(-0.941 ≤ z ≤ 0.235)

We'll use data from the normal probability table for these probabilities

P(5000 ≤ L ≤ 6000) = P(-0.941 ≤ z ≤ 0.235)

= P(z ≤ 0.235) - P(z ≤ -0.941)

= 0.593 - 0.173 = 0.420

c) The company states that 90% of the light bulbs have a lifetime of at least k hours. Find the value of k. Give your answer correct to the nearest hundred.

P(L ≥ k) = 90% = 0.9

assuming that the z-score of k is z'

P(L ≥ k) = P(z ≥ z') = 0.90

P(z ≥ z') = 1 - P(z < z') = 0.9

P(z < z') = 0.1

Using the normal distribution table

z' = -1.282

z' = (k - μ)/σ

-1.282 = (k - 5800)/850

k = (-1.282 × 850) + 5800 = 4710.3 = 4700 hours to the nearest hundred.

Hope this Helps!!!

You might be interested in
How many ways can 8 different gifts be given to 5 diffrent children with each children recieving onegift?
Delicious77 [7]

8\cdot7\cdot6\cdot5\cdot4=6,720

5 0
3 years ago
What is the length of the diameter?
olga nikolaevna [1]

is there any instructions above the circle?

4 0
3 years ago
Read 2 more answers
In the Itty Bitty High School, there are 85 students. There are 27 students who take French, 51 who take Geometry and 38 who tak
andrew-mc [135]

Answer:

58 students

Step-by-step explanation:

Given

Total = 85

French = 27

Geometry = 51

History = 38

None = 5

All = 2

Required

Students that take only 1 subjects

The attached image illustrates the question.

For French only (x), we have:

x + 7 -2+10-2+2=27

x + 15=27

Collect like terms

x =- 15+27

x =12

For Geometry only (y), we have:

y+10-2+15-2+2=51

y+23=51

Collect like terms

y=-23+51

y=28

For History only (z), we have:

z +15-2+7-2+2=38

z +20=38

Collect like terms

z =-20+38

z =18

Students with one subject is then calculated as:

1\ subject = x+y+z

1\ subject = 12 + 28 + 18

1\ subject = 58

5 0
3 years ago
Can some one awser some of those please thank you please :)
Alexeev081 [22]
5. 1,000,000
6. 9,300
7. 5,070
8. 5, 280
9. 810
10. 220
11. 44,770
12. 76, 000

Those are a few answers for you. Try looking back at your notes (If you copied any) to figure out your problems :)
4 0
3 years ago
Read 2 more answers
Help (easy question)<br> *attachment below*
JulsSmile [24]

Answer:

total ground and wall angle is 90°

beam angle with ground= 51

beam angle with wall =39

because total angle=angle with ground + angle with wall

angle with wall=total angle-angle with ground

angle with wall= 90-51=39

8 0
3 years ago
Other questions:
  • What is the total surface area of the square pyramid below? <br><br>question above <br>​
    9·1 answer
  • Can you use the law of syllogism and why?
    14·1 answer
  • Which expression is equivalent tos cos(3x)sinx
    5·2 answers
  • Please Help Me!!!!!!!
    5·2 answers
  • What is the answer I really need help with this hepl
    9·2 answers
  • Solve for x. (Geometry)
    11·2 answers
  • Colton makes the claim to his classmates that less than 50% of newborn babies born this year in his state are boys. To prove thi
    12·1 answer
  • Graph the inequality -5x +2≤27
    10·2 answers
  • A cookie recipe calls for 2 cups of m&amp;m's to make 12 cookies. How many cups of m&amp;m's are needed to make 84 cookies
    8·1 answer
  • 9.8x10^6 In standard form
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!