A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a standard deviation of 86 minutes with a mean life of 505 minutes. Of the claim is true, in a sample of 120 batteries, what is the probability that the mean battery life would be greater than 523.8 minutes

Answers

Answer 1

Answer:

0.0082 = 0.82% probability that the mean battery life would be greater than 523.8 minutes

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Standard deviation of 86 minutes with a mean life of 505 minutes.

This means that [tex]\sigma = 86, \mu = 505[/tex]

Sample of 120:

This means that [tex]n = 120, s = \frac{86}{\sqrt{120}}[/tex]

What is the probability that the mean battery life would be greater than 523.8 minutes?

This is 1 subtracted by the p-value of Z when X = 523.8. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{523.8 - 505}{\frac{86}{\sqrt{120}}}[/tex]

[tex]Z = 2.39[/tex]

[tex]Z = 2.39[/tex] has a p-value of 0.9918.

1 - 0.9918 = 0.0082

0.0082 = 0.82% probability that the mean battery life would be greater than 523.8 minutes


Related Questions

if a +b+c = 0 then the value of a²+b²+c²/bc+ca+ab

pls solve and give the explanation​

Answers

Answer:

[tex]\frac{a^2 + b^2 +c ^2}{a*b + a*c + b*c} = -2[/tex]

Step-by-step explanation:

if:

a + b + c = 0

then we can rewrite:

c = -a - b

Now we can replace this in our expression:

[tex]\frac{a^2 + b^2 + c^2}{a*b + a*c + b*c} = \frac{a^2 + b^2 + (-a - b)^2}{a*b + a*(-a - b) + b*(-a - c)}[/tex]

Now we can rewrite:

(-a - b)^2 = a^2 + 2*a*b + b^2

Then we can rewrite our expression as:

[tex]\frac{a^2 + b^2 + a^2 + b^2 + 2*a*b}{a*b - a^2 - a*b - b^2 - b*a}[/tex]

Let's keep simplifying this:

[tex]\frac{2*(a^2 + b^2 + a*b)}{-a*b - b^2 - a^2}[/tex]

Here is easy to see the simplification we need to do, as we have the same factor in the denominator as in the numerator (just a different of sign).

[tex]\frac{2*(a^2 + b^2 + a*b)}{-a*b - b^2 - a^2} = \frac{2*(a^2 + b^2 + a*b)}{-(a^2 + b^2 + a*b)} = -2[/tex]

Then the expression is equal to -2

[tex]\frac{a^2 + b^2 +c ^2}{a*b + a*c + b*c} = -2[/tex]

x+2=5, what must x equal? how did you know this

Answers

Answer:

x=3 because 5-2=3 meaning 3+2=5

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

x+2-2=5-2

x=3

subtract 2 from both sides of the equation

Maria is bringing her sick dog Pedro in for a series of appointments at the
veterinary clinic. Her total cost over the course of treatment will be $150 for tests
and medicine plus $30 per appointment, a.

Answers

Answer:

need help asap

Step-by-step explanation:

X=130+50a is the correct answer

Which fraction is equivalent to 2/6?​

Answers

1/3 2/6 3/9 4/12 … ignore this i need 20 letters

Find the equation of a line that passes through (5.3) and (4,5).

Answers

Answer:

y=-2x+13

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(5-3)/(4-5)

m=2/-1

m=-2

y-y1=m(x-x1)

y-3=-2(x-5)

y=-2x+10+3

y=-2x+13

5 people are sharing 14 kilograms of peaches. How many kilograms of peaches will each person receive?

A) 1 4 5 kilograms Eliminate B) 14 5 kilograms C) 5 14 kilograms D) 1 14 kilograms

Answers

Answer:

Each person would receive 2.8 kilograms of peaches.

pls help me rn i really need help i will give 10 points

Answers

The height would be 13 inches


Helpp ASAP. Due at 11:59 and I don’t understand none of it

Answers

Answer:

its 504 ok...........................

Hope It Helps

504. If you multiply all the numbers together, you get all the possible combinations of such events

Directions: Find the surface area of the following solid figures using the given
formula Fill in the blank with the missing number.


(help, i have many assignments to do)​

Answers

Answer:

for number 2:

(6cm x 4cm) + (6cm x 3cm)

24cm + 18cm + 12cm

2 x 54cm

108cm

for number 3:

80m + 1920m

2,000m

plzzzzz help me i have no clue​

Answers

Answer: Maybe a

Step-by-step explanation:

I mean it is confusing but still look over it

Answer:

The bottom one looks correct

Step-by-step explanation:

Any number from 1-infinity will make that true

How do I write -x + 2y= -4 in slope intercept form

Answers

Answer:

ok so slope intercept for is y=mx+b, or y=slope x + y intercept. Sooo it would be y=0.5x-2 :) hope this helps

Step-by-step explanation:

Answer:

y = 1/2 x - 2

Step-by-step explanation:

Slope-intercept form:

y = mx + b

You need to solve for y.

-x + 2y = -4

2y = x - 4

y = 1/2 x - 2


A. 152 + 192
OB. 15+19
c. 15+19
D. 162 +19

Answers

Answer:

By using the pythagorean theorem a^2 + b^2 = c^2

D is the correct answer Where PQ

= √15^2+√19^2

=√ 225 + √361

= √ 586

Length of PQ = √586 = 24.2074368738(ans)

Oh I did this before here a the part that I did hope I helped !!! The photo did not fit fell but ya

Length = 4
Width = ?
Area = 60

Answers

Answer:

the width is 15

Step-by-step explanation:

What value of x satisfies this equation?

10(1.5)^(3x) = 80

Round your answer to the nearest hundredth.


Answers

Answer:

X = 1.71

or

X = 1.70951

Step-by-step explanation:

Good Luck!

The required value of x for the given equation is approximately 1.71.

What are exponential functions?

When the expression of function is such that it involves the input to be present as exponent (power) of some constant, then such function is called exponential function. There usual form is specified below. They are written in several such equivalent forms.

Equation:

The given equation is [tex]10(1.5)^{3x} = 80[/tex]

Divide both sides by 10.

[tex](1.5)^{3x} = \dfrac{80}{10}\\\\(1.5)^{3x} = 8[/tex]

Taking log on both sides, we get

[tex]log (1.5)^{3x} = log 8\\\\3x log (1.5) = log 8[/tex]

Divide both sides by 3log(1.5).

x = log 8/ 3log(1.5)

x = 1.71

Therefore, the required value of x for the given equation is approximately 1.71.

Find out more about 'Equation' here:

brainly.com/question/11162571

#SPJ2

1. Elizabeth wrote the quadratic function y = -3(x-6). What is the same equation written in standard form?​

Answers

y = -3(x - 6)

y = -3x + 18

3x + y = 18

3x + y =18
(correct me if wrong)

y = 3x - 3 y = x2 + 5x - 2

Answers

Answer:

The answer is

(0 , 0)

Good luck!

Is 5pi/3 the same as 5/3 radians?

Best answer gets brainliest!!

Answers

Hey hope you have a great day today

Consider the following equation. Graph 5x + 6y = 30
PLEASE SHOW STEPS

Answers

Answer:

Step-by-step explanation:

Convert the equation into slope-intercept form.

5x-6y =30           Subtract 5x from each side

-6y = -5x + 30     Multiply each term by -1

6y = 5x – 30       Divide each side by 6

y = ⅚x - 5

2. Create a table of different x and y values,

x        ⅚x – 5        y  

-12      ⅚(-12) – 5     -15  

-6      ⅚(-6) – 5       -10

0       ⅚(0) – 5         -5

6       ⅚(6) – 5          0

12        ⅚(12) – 5        5

3. Convert the table to ordered pairs

(-12,-15)

(-6, -10)

(0, -5)

(6, 0)

(12, -5)

4. Plot the points and draw a line through them.

Find the measure of the missing side PQ using trig ratios

Answers

Answer:

take 48 degree as reference angle

use sine rule

sin48=opposite/hypotenuse

0.74=5.4/x

x0.74=5.4

x=5.4/0.74

x=7.29  m

Step-by-step explanation:

Answer:

[tex]sin 48 = \frac{5.4}{X}\\\\X = \frac{5.4}{sin 48}= 7.27m[/tex]

HELPP, RIGHT TRIANGLES AND TRIGONOMETRY

Answers

Step-by-step explanation:

x²=6²+8²

=36+64

= 100

x=√100 = 10

Answer:

[tex]\displaystyle 10 = x[/tex]

Step-by-step explanation:

[tex]\displaystyle a^2 + b^2 = c^2 \\ \\ 8^2 + 6^2 = x^2 \hookrightarrow 64 + 36 = x^2 \hookrightarrow \sqrt{100} = \sqrt{x^2} \\ \\ \boxed{10 = x}[/tex]

We only want the NON-NEGATIVE root sinse we are measuring the length of the hypotenuse.

I am joyous to assist you at any time.

Which of the following is the point and slope of the equation y + 2 = 2(x - 8)?

-8, 2), 2


(2, -8), 2


(8, -2), 2


(-2, 8), 2

Answers

I think it would be (2,-8),2

Draw the net figure label the net with appropriate dimensions in centimeters

Answers

Answer:

your answer has to be A or B  cuz the rest fo match up with the measurements

Step-by-step explanation:

1. An object is blasted upward at an initial velocity of 320 ft/s. The height, h(t), of the object is a function of time, t (in seconds), and is given by the formula h(t) = -16t2 + 320t. How long will it take the object the hit the ground after takeoff?

Answers

Answer:

20 seconds

Step-by-step explanation:

roots are (0,0) and (20,0) so 20-0 will provide the time from takeoff to landing

Help please ❤️ !
Write a linear equation in slope intercept form given the
Slope = 2 and the y intercept = (0,-4)


Answers

Answer:

y = 2x - 4

Step-by-step explanation:

y = (slope)x + (y intersept)

y = (2)x + (-4)

y = 2x - 4

An aquarium tank that measures 2.4 meters high, 6 meters long, and 1.5 meters wide is completely filled with water. The density of water is 1,000 kilograms per cubic meter. What is the mass of the water in the tank?

A:46 kilograms

B.101 kilograms

C.9,900 kilograms

D.21,600 kilograms

Answers

Answer:

D.21,600 kilograms

Step-by-step explanation:

The volume of the tank is Length x Width x Height (6*1.5*2.4)

So the volume is 21.6 cubic meters.

Therefore, there are 21.6 cubic meters of water.

The density of water is 1,000 kg per cubic meter. So multiply 1,000 to the number of cubic meters. (1,000*21.6)

The mass of the water in the tank is 21,600 kg

Please help need this last one.

Answers

Answer:

10

Step-by-step explanation:

If you look at it closely you can see its a complete circle.... on the sides its 12 then as you go to the center the first one is ten and the dot is in the center which should make it 10.

Answer:

it's basically 10, both sides are equal

Step-by-step explanation:

Please help!!!!!!!!!!!!!!

Answers

Answer:

131/156 or about 84%

5/14 or about 36%

Step-by-step explanation:

P(<6 classes) = number of males and females not taking 6 out of total males and females, which is 131/156 or about 84%

P(M,5) = 74/156 x 20/74 which reduces to 5/14

Question 1 of 14
Which of the equations or inequalities below are true?
A. -4 + 6 = 1
B. -4 + 6 7-2
C. -4 + 6 24
D. -4+6 s 2

Answers

question seems incomplete

there are no notations for inequalities

A digital camera usually costs $700. This week it is on sale at a discount of 20%. What
is the sale price of the digital camera?

Answers

Answer:

560

Step-by-step explanation:

So we know that 20% goes into 100% 5 times.

700/5 will give you a clean 140, meaning 20% of the price is 140

Thus 700-140 and you get 560 dollars

If you have a calc you could also do 700 x .80 (since .80 is also equal to 80%) and get the same answer

A researcher investigated the relationship between alcohol intake and reaction time in a driving simulation task. Participants drank either one ounce or three ounces of alcohol and were then measured on braking speed at a simulated red light. The independent variable was the

Answers

Answer:

Alcohol intake

Step-by-step explanation:

The Independent variable also called the predictor variable may be described as the treatment which is given a subject or factors which is expected to induce a change in our measured variable which is called the predicted or dependent variable. During research, the test various factors which are expected to cause a change are the independent variable, whereas, the variable which is measured as a result of the changes caused due to the different independent variables is the dependent variable. In the scenario above, we wish to measure braking speed after the subjects have been given a certain ounce of alcohol, this ounce of alcohol is the treatment which is expected to cause a variation in the braking speed of the participants. Hence, alcohol intake is the independent variable while braking speed is the dependent variable.

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