The life of light bulbs is distributed normally. The standard deviation of the lifetime is 2525 hours and the mean lifetime of a bulb is 590590 hours. Find the probability of a bulb lasting for at most 622622 hours. Round your answer to four decimal places.

Answers

Answer 1

Answer:

0.8997 = 89.97% probability of a bulb lasting for at most 622 hours.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 590 hours, standard deviation of 25 hours.

This means that [tex]\mu = 590, \sigma = 25[/tex]

Find the probability of a bulb lasting for at most 622 hours.

This is the p-value of Z when X = 622.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{622 - 590}{25}[/tex]

[tex]Z = 1.28[/tex]

[tex]Z = 1.28[/tex] has a p-value of 0.8997.

0.8997 = 89.97% probability of a bulb lasting for at most 622 hours.


Related Questions

Describe the system of equations
How many solutions does this system have.

Answers

Answer:

Step-by-step explanation:

One solution, at the point of intersection, (3,3)

A manager records the repair cost for 14 randomly selected dryers. A sample mean of $88.34 and standard deviation of $19.22 are subsequently computed. Determine the 90% confidence interval for the mean repair cost for the dryers. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answers

Answer:

Hence the 90% confidence interval estimate of the population mean is [tex](79.24 , 97.44)[/tex]

Step-by-step explanation:

Given that,  

Point estimate = sample mean = [tex]\bar x[/tex] = 88.34  

sample standard deviation = s = 19.22  

sample size = n = 14  

Degrees of freedom = df = n - 1 = 13  

Critical value =[tex]t\alpha /2,[/tex] df = 1.771

 

Margin of error

[tex]E = t\alpha/2,df \times (\frac{s}{\sqrt{n} } )\\= 1.771 \times (19.22 / \sqrt 14)[/tex]  

Margin of error = E = 9.10  

The 90% confidence interval estimate of the population mean is,  

[tex]\bar x - E < \mu < \bar x + E\\\\88.34 - 9.10 < \mu < 88.34 + 9.10\\\\79.24 < \mu < 97.44\\(79.24 , 97.44)[/tex]

Reasoning by induction

Question 1 options:

1)

develops a general conclusion based on observations of cases.


2)

develops a general conclusion based on given information.


3)

starts with assumptions that are known to be valid to draw another new truths.


4)

uses patterns to create logical proofs.

Answers

Answer:

1because the occasion of cases

Write the point-slope form of an equation of the line through the points (-2, 6) and (3,-2).

Answers

Answer:

[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]

OR

[tex]y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]

Step-by-step explanation:

Hi there!

Point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where [tex](x_1,y_1)[/tex] is a point and [tex]m[/tex] is the slope

1) Determine the slope

[tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_2}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the given points (-2, 6) and (3,-2):

[tex]m=\frac{\displaystyle -2-6}{\displaystyle 3-(-2)}\\\\m=\frac{\displaystyle -8}{\displaystyle 3+2}\\\\m=-\frac{\displaystyle 8}{\displaystyle 5}[/tex]

Therefore, the slope of the line is [tex]-\frac{\displaystyle 8}{\displaystyle 5}[/tex]. Plug this into [tex]y-y_1=m(x-x_1)[/tex]:

[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]

2) Plug in a point [tex](x_1,y_1)[/tex]

[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]

We're given two points, (-2, 6) and (3,-2), so there are two ways we can write this equation:

[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x-(-2))\\\\y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]

OR

[tex]y-(-2)=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)\\y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]

I hope this helps!

Find the sum of the geometric series given a1=−2, r=2, and n=8.
A. -510
B. -489
C. -478
D. 2

Answers

Answer:

A. -510

Step-by-step explanation:

We are given the variable values:

a = -2r = 2n = 8

Geometric series formula:

[tex]s = \frac{a( {r}^{n} \times - 1) }{r - 1} [/tex]

Plugging in values we have:

[tex]s = \frac{ - 2( {2}^{8} - 1) }{2 - 1} [/tex]

Simplifying the equation we are left with:

[tex] \frac{ - 2(255)}{1} = - 510[/tex]

Solve for x and y…….

Answers

The shapes are the same size. Match the sides.

3x -1 = 17

Add 1 to both sides:

3x = 18

Divide both sides by 3:

X = 6

2y = 16

Divide both sides by 2

Y = 8

Answer: x = 6, y = 8

4 people take 3 hours to paint a fence assume that all people paint at the same rate How long would it take one of these people to paint the same fence?​

Answers

Answer:

12

Step-by-step explanation:

The triangles are similar.


What is the value of x?


Enter your answer in the box.

x =

Answers

Answer:

x=12

Step-by-step explanation:

each side of the smaller triangle, we can multiply by 4 to get the side of the larger triangle

ex: 8*4=32 and 17*4=68

so we can assume that 15*4= 4x+12

60=4x+12

48=4x

x=12

Answer:

x = 12

Step-by-step explanation:

The triangles are similar so we can use ratios

4x+12      32

-------  = ------------

15             8

Using cross products

(4x+12) *8 = 15 * 32

(4x+12) *8 = 480

Divide each side by 8

(4x+12) *8/8 = 480/8

4x+12 = 60

Subtract 12 from each side

4x+12 -12 = 60-12

4x = 48

Divide by 4

4x/4 = 48/4

x = 12

You wish to create a 5 digit number from all digits; 0 1 2 3 4 5 6 7 8 9
Repetition is not allowed
* 0 cannot be first as it does not count as a place value if it is first. Ie. 027 is a 2 digit number

How many even numbers can you have?

Answers

Answer:

10234

Step-by-step explanation:

one is the smallest number so its first

and then you can place zero

after that just place the second smallest number

and so on


The population, P(t), in millions, of a country, in year t, is given by the formula P(t) = 24 + 0.4t. What are the values of the population for t = 10, 20,
and 30?

Answers

Answer:

B. 28, 32, 36 millions

Step-by-step explanation:

Given:

P(t) = 24 + 0.4t

Where,

P(t) = population in millions

t = number of years

✔️Value of the population when t = 10:

Plug in t = 10 into P(t) = 24 + 0.4t

P(t) = 24 + 0.4(10)

P(t) = 24 + 4

P(t) = 28 million

✔️Value of the population when t = 20:

Plug in t = 20 into P(t) = 24 + 0.4t

P(t) = 24 + 0.4(20)

P(t) = 24 + 8

P(t) = 32 million

✔️Value of the population when t = 30:

Plug in t = 30 into P(t) = 24 + 0.4t

P(t) = 24 + 0.4(30)

P(t) = 24 + 12

P(t) = 36 million

Lost-time accidents occur in a company at a mean rate of 0.8 per day. What is the probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2

Answers

Answer:

0.01375 = 1.375% probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2.

Step-by-step explanation:

We have the mean during the interval, which means that the Poisson distribution is used.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

Lost-time accidents occur in a company at a mean rate of 0.8 per day.

This means that [tex]\mu = 0.8n[/tex], in which n is the number of days.

10 days:

This means that [tex]n = 10, \mu = 0.8(10) = 8[/tex]

What is the probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2?

This is:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-8}*8^{0}}{(0)!} = 0.00034[/tex]

[tex]P(X = 1) = \frac{e^{-8}*8^{1}}{(1)!} = 0.00268[/tex]

[tex]P(X = 2) = \frac{e^{-8}*8^{2}}{(2)!} = 0.01073[/tex]

So

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.00034 + 0.00268 + 0.01073 = 0.01375[/tex]

0.01375 = 1.375% probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2.

Solve 8x + c = k for x

Answers

Answer:

x = 1/8(k-c)

Step-by-step explanation:

8x + c = k

Subtract c from each side

8x +c-c = k-c

8x = k-c

Divide each side by 8

8x/8 = (k-c)/8

x = 1/8(k-c)

Answer:

x-1/8(k-c)

Step-by-step explanation:

Ethan buys a video game on sale. If the video game usually costs $60, and it was on sale for 20% off, how much did Ethan pay? Round to the nearest whole dollar.

Answers

Ethan will pay $31.99 with the discount.

How? This is the answer because:

If 39.99 is 100%, and you are trying to find 20%...

1. you need to set it up as a ratio (of course, you do not need to do this, but it is easier for me to do it this way)

2. the ratio will look like this: 39.99/100% x/20%

3. all we need to do from here is to cross multiply!

4 39.99 x

---------- = ----------

100 20

-price is on the top and percent on the bottom

-you would now do 39.99 times 20

-then divide by 100

5. once you have 20% of 39.99, you need to subtract that answer from the total

6. 39.99 - 7.998 = 31.992 (you need to round to the nearest hundredth)

Hope this helps <3

Is the answer right?

Answers

Answer:

one solution.. your answer is correct

Step-by-step explanation:

discriminate = 900 - (4*9*25)  = 0

thus only one solution

your answer is correct

A market surveyor wishes to know how many energy drinks teenagers drink each week. They want to construct a 98% confidence interval for the mean and are assuming that the population standard deviation for the number of energy drinks consumed each week is 1.1. The study found that for a sample of 1027 teenagers the mean number of energy drinks consumed per week is 5.9. Construct the desired confidence interval. Round your answers to one decimal place.

Answers

Answer:

The 98% confidence interval for the mean number of energy drinks consumed per week by teenagers is (5.8, 6).

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.327\frac{1.1}{\sqrt{1027}} = 0.1[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 5.9 - 0.1 = 5.8 drinks per week.

The upper end of the interval is the sample mean added to M. So it is 5.9 + 0.1 = 6 drinks per week.

The 98% confidence interval for the mean number of energy drinks consumed per week by teenagers is (5.8, 6).

REVISED 2/3/
the following using the picture below.
4
a) Two pairs of supplementary angles:
b) A pair of complementary angles:







Please explain this! Thank you!

Answers

Supplementary angles are those angles which make a sum of 180°.

Complementary angles are those angles which make a sum of 90°.

The supplementary angles are given by the straight lines making angles of 180°.

There are two straight lines CB and DE

The angles DAF and FAE are the two angles making a straight line DE

The angles CAF and FAB are the two angles making a straight line CB

The complementary angles are given by angles formed between the perpendicular lines making angles of 90°.

Angle BAF is formed by angle BAE and angle AEF

Supplementary Angle given by the straight line DE is formed by the angles DAF and FAE.

Complementary Angle BAF is formed by angle BAE and angle AEF.

https://brainly.com/question/12919120

Simplify
x * x^5 / x^2 * x

Answers

it’s x^3, i guess hope this helps

Which one is greater 4.5% or 0.045

Answers

Answer:

They are equal

Step-by-step explanation:

4.5% is 0.045 in decimal form

Answer: They are equal

Step-by-step explanation:

I always remember by taking the two o's in percent and moving them two spots to the left and vise versa if you want to make a decimal into a percent  (move it two spots to the right).

If 4 gallons of gasoline cost $13.76, how much will 11 gallons of gasoline cost?

Answers

Answer:

x=37.84

Step-by-step explanation:

We can write a ratio to solve

4 gallons        11 gallons

--------------- = ----------------

13.76              x dollars

Using cross products

4x = 11*13.76

4x=151.36

Divide by 4

4x/4 = 151.36/4

x=37.84

Round each of the following numbers to four significant figures and express the result in standard exponential notation: (a) 102.53070, (b) 656.980, (c) 0.008543210, (d) 0.000257870, (e) -0.0357202

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

Rounding each number to 4 significant figures and expressing in standard notation :

(a) 102.53070,

Since the number starts with a non-zero, the 4 digits are counted from the left ;

102.53070 = 102.5 (4 significant figures) = 1.025 * 10^2

(b) 656.980,

Since the number starts with a non-zero, the 4 digits are counted from the left ; the value after the 4th significant value is greater than 5, it is rounded to 1 and added to the significant figure.

656.980 = 657.0 (4 significant figures) = 6.57 * 10^2

(c) 0.008543210,

Since number starts at 0 ; the first significant figure is the first non - zero digit ;

0.008543210 = 0.008543 (4 significant figures) = 8.543 * 10^-3

(d) 0.000257870,

Since number starts at 0 ; the first significant figure is the first non - zero digit ;

0.000257870 = 0.0002579 (4 significant figures) = 2.579 * 10^-4

(e) -0.0357202,

Since number starts at 0 ; the first significant figure is the first non - zero digit ;

-0.0357202 = - 0.03572 (4 significant figures) = - 3.572* 10^-2

Please helppppppppp!!!!

Answers

Terminal point for 4π/3

(cos4π/3 ,sin4π/3)

{cos(π+π/3) ,sin(π+π/3)}= (-cosπ/3 ,-sinπ/3)

or ,(- 1/2, -√3/2)

OPTION C

A graph of 2 functions is shown below. graph of function f of x equals negative 11 by 3 multiplied by x plus 11 by 3 and graph of function g of x equals x cubed plus 2 multiplied by x squared minus x minus 2 Which of the following is a solution for f(x) = g(x)? (2 points) x = −2 x = 1 x = 0 x = −1

Answers

9514 1404 393

Answer:

  (b)  x = 1

Step-by-step explanation:

A graph shows the solution to f(x) = g(x) is x = 1.

__

We want to solve ...

  g(x) -f(x) = 0

  x^3 +2x^2 -x -2 -(-11/3x +11/3) = 0

  x^2(x +2) -1(x +2) +11/3(x -1) = 0 . . . . . factor first terms by grouping

  (x^2 -1)(x +2) +11/3(x -1) = 0 . . . . .  . the difference of squares can be factored

  (x -1)(x +1)(x +2) +(x -1)(11/3) = 0 . . . . we see (x-1) is a common factor

  (x -1)(x^2 +3x +2 +11/3) = 0

The zero product rule tells us this will be true when x-1 = 0, or x = 1.

__

The discriminant of the quadratic factor is ...

  b^2 -4ac = 3^2 -4(1)(17/3) = 9 -68/3 = -41/3

This is less than zero, so any other solutions are complex.

How do I figure this question out

Answers

Answer:

Orthocenter would be in the middle of the shape.

Step-by-step explanation:

B.

PLS
Write the equation of the piecewise function that is represented by its graph.

IS IT A, B, C, OR D

Answers

9514 1404 393

Answer:

  a) domain bounds are -1 ≤ x ≤ 1, x > 1

Step-by-step explanation:

In considering the definition of any piecewise function, the domain descriptions in the function definition must match the pieces shown in the graph.

Here, the right segment has no upper bound, so x > 1 is an appropriate description of its domain.

The left segment has the points at x=-1 and x=1 included, so the appropriate domain description for that is -1 ≤ x ≤ 1.

The one answer choice that combines these domain descriptions is ...

  [tex]\displaystyle f(x)=\begin{cases}x^2,&\text{if }-\!1\le x\le1\\\sqrt{x},&\text{if }x>1\end{cases}[/tex]

Zoe has 4 pounds of strawberries to make pies. How many ounces of strawberries Is this?
64 oz.
60 oz.
68 oz.
72 oz.

Answers

Answer: 64 ounces (choice A)

Work Shown:

1 pound = 16 ounces

4*(1 pound) = 4*(16 ounces)

4 pounds = 64 ounces

Riley wants to make 100ml of 25% saline but only has access to 12% and 38% saline mixtures. x= 12% y=38%

Answers

Answer:

x = 50

y = 50

Step-by-step explanation:

[tex]\begin{bmatrix}x+y=100\\ 0.12x+0.38y=25\end{bmatrix}[/tex]

.12(100-y) + .38y = 25

x = 50

y = 50

Hari earns Rs 4300 per month. He spends 80% from his income. How much amount does he save in a year? ​

Answers

Answer:

Hari saves $ 10,320 in a year.

Step-by-step explanation:

Given that Hari earns $ 4300 per month, and he spends 80% from his income, to determine how much amount does he save in a year, the following calculation must be performed:

100 - 80 = 20

4300 x 0.20 x 12 = X

860 x 12 = X

10320 = X

Therefore, Hari saves $ 10,320 in a year.

I need help ASAP please no links

Answers

Answer: D' = (1, -1)

Step-by-step explanation:

When dilating by a 1/2 you take a point and divide the x and y of the point in half. So D before is (2,-2) and then divide that by a 1/2, which gives us our answer (1, -1).

Complete the sentence that explains why Write an Equation is a reasonable strategy for solving this problem. Because the answer may be _________ the numbers in the problem.

Answers

Answer:

4 e

Step-by-step explanation:

dz6dxrx xrrx6 xz33x4xr4x xrx

Function below, choose the correct description of its graph.
vertical
line
horizontal
line
line with a
negative
slope
line with a parabola
positive opening
slope down
O
O
O
O
O
h(x)=0
k(x) = 4x2 +312
f(x) = x-1
O
o
o
O
O
O

Answers

Step-by-step explanation:

I think something went wrong with the answer options you provided. and maybe with the problem statement itself.

I see 3 function definitions.

I can tell you what they are and use the provided option phrasing as closely as possible :

h(x) = 0 is a horizontal line (in fact the x-axis)

k(x) = 4x² + 312 is a parabola with the opening upwards

f(x) = x - 1 is a line with positive slope (going from left to right the line goes up)

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