MATHEMATICS COLLEGE

The lifetime of a certain type of battery is normally distributed with a mean value of 10 hours and standard deviation of 2 hours. Find the probability that a randomly selected battery has a lifetime greater than 12 hou g

Answers

Answer 1

Answer:

Answer:

$P(X>12)=P((X-\mu)/(\sigma)>(12-\mu)/(\sigma))=P(Z>(12-10)/(2))=P(z>1)$

And we can find this probability using the complement rule:

$P(z>1)=1-P(z<1)$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(z>1)=1-P(z<1)=1-0.841=0.159$

Step-by-step explanation:

Previous concepts

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the lifetime of a certain type of battery of a population, and for this case we know the distribution for X is given by:

$X \sim N(10,2)$

Where $\mu=10$ and $\sigma=2$

We are interested on this probability

$P(X>12)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=(x-\mu)/(\sigma)$

If we apply this formula to our probability we got this:

$P(X>12)=P((X-\mu)/(\sigma)>(12-\mu)/(\sigma))=P(Z>(12-10)/(2))=P(z>1)$

And we can find this probability using the complement rule:

$P(z>1)=1-P(z<1)$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(z>1)=1-P(z<1)=1-0.841=0.159$

Related Questions

What is x? The degree of the angle of x
What is 2/3 - 1/2 = in simplest form
a technician charges 25$ per hour plus 50$ for a house call to repair home computers. make a table and a graph to show the cost for 1,2,3, and 4 hours of home computer repair service. is there a direct variation?
In the diagram, how many pairs of vertical angles are shown?
35 x 2/7 14, 5, 7, 10,

WILL GIVE BRAINLIEST FOR THE RIGHT ANSWER!!!

Answers

ANSWE,LET two numbers be A and B then

A+B=52

A-B=14....linear equation in 2 variable

adding 2 eqns

2A=66... dividing both side by 2

A=33

and put A=33 in eqn A+B=52

B=52-33

B=19.

SO. LARGER NUMBER=33

Smaller number=19

30 points!!!To convert measurements in the metric system, you can move the decimal point left or right. Why does this work? The metric system only uses decimal numbers. Converting in the metric system does not involve multiplication or division. The metric system is based on powers of 10. The metric system does not have conversion factors.

Answers

Answer:

its c trust me :)

Step-by-step explanation:

What is the solution to the system of equations y = -4/5x + 6 and y = -30A) (45,-30)
B) (-30,30)
C) (-30,45)
D) (30,-30)

Answers

Hi There!

Answer: A) (45,-30)

Why: x = 45 and y = -30

-30 = -4/5(45) + 6

-30 = -36 + 6

-30 = -30

Hope This Helps :)

Answer:

A is the correct answer

Step-by-step explanation:

took the exam

Which of the following ratios is equivalent to 12/20? Answers A. 3/10 B. 5:3 c. 120 to 200 D. 60/80

Answers

A is 3/10 , if we multiply top and bottom by 4 we get 12/40 , which is not equivalent to 12/20.

B is 5:3 , it cannot be equivalent to 12/20.

C is 120 to 200 , if we divide both numerator and denominator by 10 we get 12/20, So option C is correct.

D is 60/80 , if we divide both numerator and denominator by 5, we get 12/16 , which is not equivalent to 12/20.

Hence option C is the correct answer.

12 : 20
12 x 10 : 20 x 10
120 : 200 (Answer C)

Question5°F - 32)

The function to convert Fahrenheit to Celsius is °C = (°F) =

The inverse function will

9

convert Celsius to Fahrenheit. What is the inverse function? Complete the explanation of how

determining this inverse is different than determining the previous inverses.

The inverse function is °F = -(°C)=

The F and °C (select) V need to be switched like the x and y did in the previous functions.

(select) degree measures, and because of the real-world relationship, switching them

(select) ✓ make sense.

Answers

Answer:

$F = (9C + 32)/(5)$

Step-by-step explanation:

Given

$C = ((5F - 32))/(9)$

Required

Determine the inverse function

$C = ((5F - 32))/(9)$

Make F the subject of formula:

Multiply through by 9

$9C = 5F - 32$

Add 32 to both sides

$9C + 32= 5F$

Divide through by 5

$(9C + 32)/(5)= F$

$F = (9C + 32)/(5)$

The inverse function is °F = (9/5 * °C) + 32.

To determine this inverse function, we first need to understand that it's the reverse conversion from Celsius to Fahrenheit. In the original conversion from Fahrenheit to Celsius, we subtracted 32 from the Fahrenheit temperature and then divided the result by 9/5 (or 1.8).

To find the inverse, we need to do the opposite operations in reverse order. First, we need to undo the division by 1.8, which is equivalent to multiplying by 5/9. Then, we need to undo the subtraction of 32 by adding 32 to the result.

This process is different from determining previous inverses because it involves reversing the operations in the opposite order and with different constants (5/9 and 32) compared to the original function.

The F and °C variables need to be switched in the inverse function because we are now going from Celsius to Fahrenheit, and the relationship between these temperature scales requires different mathematical operations.

Switching them makes sense because it aligns with the real-world relationship between the two temperature scales and ensures that the inverse function correctly converts from Celsius to Fahrenheit

for such more questions on Inverse function

brainly.com/question/35509335

#SPJ3

There are 5 times as many females as males on the maths course at university. What fractionof the course are male?
Give your answer in its simplest form