A new car battery is sold with a two-year warranty whereby the owner gets the battery replaced free of cost if it breaks down during the warranty period. Suppose an auto store makes a net profit of $20 on batteries that stay trouble-free during the warranty period; it makes a net loss of $10 on batteries that break down. The life of batteries is known to be normally distributed with a mean and a standard deviation of 40 and 16 months, respectively.

Required:
a. What is the probability that a battery will break down during the warranty period?
b. What is the expected profit of the auto store on a battery?
c. What is the expected monthly profit on batteries if the auto store sells an average of 500 batteries a month?

Answers

Answer 1

Answer:

a) 0.1587 = 15.87% probability that a battery will break down during the warranty period.

b) The expected profit of the auto store on a battery is of $15.239.

c) The expected monthly profit on batteries if the auto store sells an average of 500 batteries a month is of $7,619.50.

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.

The life of batteries is known to be normally distributed with a mean and a standard deviation of 40 and 16 months, respectively.

This means that [tex]\mu = 40, \sigma = 16[/tex]

a. What is the probability that a battery will break down during the warranty period?

Two year warranty, that is, 24 months. This probability is the pvalue of Z when X = 24. So

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

[tex]Z = \frac{24 - 40}{16}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a pvalue of 0.1587.

0.1587 = 15.87% probability that a battery will break down during the warranty period.

b. What is the expected profit of the auto store on a battery?

1 - 0.1587 = 0.8413 probability of a profit of $20.

0.1587 probability of a loss of $10. So

[tex]E = 0.8413*20 - 0.1587*10 = 15.239[/tex]

The expected profit of the auto store on a battery is of $15.239.

c. What is the expected monthly profit on batteries if the auto store sells an average of 500 batteries a month?

Multiplying the average for a battery by 500. So

15.239*500 = $7,619.50

The expected monthly profit on batteries if the auto store sells an average of 500 batteries a month is of $7,619.50.


Related Questions

Find the volume of the following figures with the given dimension

Answers

Answer:

[tex]V=192\ in^3[/tex]

Step-by-step explanation:

Given that,

The area of base, A = 24 in²

The height of the pyramid, h = 8 in

We need to find the volume of the following figure.

The volume of pyramid is given by :

[tex]V=A\times h[/tex]

Substitute all the values,

[tex]V=24\times 8\\\\=192\ in^3[/tex]

So, the volume of the pyramid is equal to [tex]192\ in^3[/tex].

PLEASE HURRYYYYYYYYY​

Answers

Answer:

12r ft

Step-by-step explanation:

you're welcome have a nice day

In certain parts of the world tuberculosis (a very treatable and curable illness) is present in 25% of the people. If a simple chest X-ray can be used as a diagnostic tool with an accuracy of 99% detection of TB if it is present. Only in 0.5% of the cases, normal people get a positive diagnosis. 2 If a person is selected at random and the diagnosis is positive, what is the probability that the person is actually infected.

Answers

Answer:

0.9851 = 98.51% probability that the person is actually infected.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Positive test

Event B: Infected

Probability of a positive test:

99% of 25%(People have the disease).

0.5% of 100 - 25 = 75%(People do not have the disease). So

[tex]P(A) = 0.99*0.25 + 0.005*0.75 = 0.25125[/tex]

Probability of a positive test and being infected:

99% of 25%, so:

[tex]P(A \cap B) = 0.99*0.25 = 0.2475[/tex]

What is the probability that the person is actually infected?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.2475}{0.25125} = 0.9851[/tex]

0.9851 = 98.51% probability that the person is actually infected.

7)
Barry has several horses in a field. The
fence around the field is in the shape of
a rectangle. The width is 8 kilometers
and the length is 15 kilometers. The
length of the diagonal is
A 16 km
B 17 km
C 19 km
D 23 km

Answers

Answer:

I think the answer should be D) 23 km but if its wrong my bad

Step-by-step explanation:

determine the radius of a circle whose circumfrence is 16.52cm​

Answers

Answer:

radius=2.62cm

hope it helps.

Determine the scale factor for triangle ABC to Triangle A'B'C'.

Answers

D. 1/2 due to the fact that 10 would be over 20 so 10/20 and simplified is 1/2.

A square has a diagonal measuring 19 centimeters in length.which of the following is closest to the length of each side of the square?

Answers

Answer:

13cm

Step-by-step explanation:

Let the length of each side be x;

Using the pythagoras theorem

l² = x² + x²

l is the length of the diagonal

l² = 2x²

19² = 2x²

361 = 2x²

x² = 361/2

x² = 180.5

x =√180.5

x = 13

hence the length of each side of the square is closest to 13cm

if 12+ blank=0+12, than blank must equal

Answers

0. 12+0=0+12 blank is 0.
Blank would have to equal zero

Maori created this shape out of construction paper using a ruler and scissors. She made sure that all of her angles were right angles.
What is the area of Maori's shape?

A) 36 cm2
B) 48 cm2
C) 90 cm2
D) 102 cm2

Answers

Answer:

B) 48cm²

Step-by-step explanation:

find the area of the 2 rectangles

A = bh

A = 9×4

A = 36

A = bh

A = 6×2

A = 12

add them up you get 48cm²

Please help me with this

Answers

Answer: you should study, plus give me brainliest please. lol

Step-by-step explanation:

and the other answer might be a bot sending links to websites with malware, please dont .open the link unless you want malware on your device, if its fake. and you cant make websites/ links just to post answers. this is a warning.

area of circle if circumference is 132m

Answers

Answer:

1386 cm²

Step-by-step explanation:

Here's your answer!

Hope it helps :)

Answer:

1386.56m²

Step-by-step explanation:

A=C2

Circumference^2/4(3.14)

Which function is graphed below?



Answers

The answer for the question above is the B/Second one or

Y=3(1/3)^x


[tex](4.56 \times 3.6) \div 0.12[/tex]

Answers

The right answer is 136.8

The perimeter of a rectangle measures 26 in. Find the other
side length, if one side measures 4 in.

Answers

the other side length is 9in
the rectangle is 26 in and a giving measure is 4 in. so 4+4=8 (8 is the total of two measures). then u do 26-8 and u get 18. (18 is the total of 2 sides). you are tying to find one so u divide it by 2 and you get 9

Jake bought 4.08 pounds of apples. He knows that 1.19 pounds are Gala apples and the rest are Cameo apples. How many pounds of Cameo apples did he buy? A 2.89 B 3.11 C 3.89 D5.27​

Answers

Answer:

2.89

Step-by-step explanation:

4.08-1.19 = 2.89

you just do simple subtraction

Answer:

A. 2.89 pounds

Step-by-step explanation:

4.08 pounds of apples all together subtract the Gala apples 1.19 pounds and you'll get that Jake bought 2.89 pounds of Cameo apples.

4.08 - 1.19 = 2.89

An ordinary (fair) die is a cube with the numbers through on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment. Compute the probability of each of the following events. Event : The sum is greater than . Event : The sum is not divisible by .

Answers

Complete question :

Compute the probability of each of the following events.

Event : The sum is greater than 6

Event : The sum is not divisible by 2

Answer:

7/12 ; 1/2

Step-by-step explanation:

Sample space :

2, 3, 4, 5, 6, 7

3, 4, 5, 6, 7, 8

4, 5, 6, 7, 8, 9

5, 6, 7, 8, 9, 10

6, 7, 8, 9, 10, 11

7, 8, 9, 10, 11, 12

Probability that sum is greater than 6:

Number of outcomes greater Than 6 = required outcomes = (7,7,7,7,7,7,8,8,8,8,8,9,9,9,9,10,10,10,11,11,12) = 21

Total sample space = total possible outcomes = 36

Probability = required outcome / Total possible outcomes

P(sum is greater Than 6) = 21 / 36

2.)

Obtaining an even number :

Sum not divisible by 2 = required outcomes = (3, 5, 7, 3, 5, 7, 5, 7, 9, 5, 7, 9, 7, 9, 11, 7, 9, 11) = 18

Total sample space = total possible outcomes = 36

P(sum is not divisible by 2) = 18 / 36 = 1 / 2

i will be sooooo thankful if u helped me

Answers

the answer to question 35 is d

Answer:

For 35 its C

Step-by-step explanation:

 

4. Complete the number sentence below: *
x 102 = 2,500
Help me please !!!

Answers

The answer is 25 because if you go threw and put all the answers in a calculator 25x10^2=2,500

The diagram shows the diameter of the opening
of a waffle ice cream cone.
18 cm
Which of the following is closest to the area of
the opening in square centimeters?
A.
1,017.88 cm2
C. 254.47 cm
B.
56.55 cm2
D. 28.27 cm2
I will give brainleist

Answers

Answers

D 36

Step-by-step explanation:

77 is the area for the squared trapezoid and 36 is the closest to 77

What is 2x10-50=x and I’m just typing this to get to 20 words or whatever

Answers

Step-by-step explanation:

sorry I don't know the answer I want some points so because I do this I really really sorry. and thanks for point

In the summer time your friend wants to have a snow cone stand at a local grocery store parking lot. You want to make sure he actually makes money. The grocery store charges $300 per month. All products are calculated to be 25 cents per customer. Your plans are to sell each cone for $1.25.

a. Write a mathematical expression representing the cost of operation for a month.
b. Write a mathematical expression representing sales.
c. Create an equation that will represent overall profit of the operation for a month.
d. Simplify the equation into slope intercept form and standard form. What is the slope and explain its meaning in the context of selling snow cones? What is the intercept and what is its meaning?
e. Describe the method of graphing the slope intercept form and also the standard form of the equation.
f. What is the domain and range of the equation? Is the relation a function, why?
g. How many snow cones do you need to sell to break even in the first month?
h. How much is the profit if you sell 425, 550 or 700 snow cones in the first month of business?

Answers

Answer:

31.25 is the answer at your question

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frrref? I think'nt,


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Answers

Answer:

ooo

Step-by-step explanation:

fr SHEEEEEEEEEEEEEEEEESH

hey yall i would really appreciate your help on this plz

Answers

Answer:

the length of the opposite side (x), is 27.2

Step-by-step explanation:

For the given right triangle problem;

the opposite side of the given angle, opp. = 22

the hypothenuse side,  hypo. = x

given angle of the triangle, θ = 54⁰

The length of the opposite side (x), is calculated as follows;

[tex]sin \ \theta = \frac{opp.}{hypo.} \\\\sin (54) = \frac{22}{x} \\\\x = \frac{22}{sin(54)} \\\\x = 27.2[/tex]

Therefore, the length of the opposite side (x), is 27.2

The area of a rectangle is 48ft2. The length is 3 times the width. Which of the following equations can be used to solve for the width?

Answers

Answer:

Width of rectangle = 4 ft

Step-by-step explanation:

Given:

Area of rectangle = 48 ft²

Length of rectangle = 3[Width of rectangle]

Find:

Width of rectangle

Computation:

Assume;

Width of rectangle = a

So,

Length of rectangle = 3[Width of rectangle]

Length of rectangle = 3a

Area of rectangle = l x b

48 = 3a x a

3a² = 48

a² = 16

a = 4

Width of rectangle = 4 ft

Length of rectangle = 3[Width of rectangle]

Length of rectangle = 3[4]

Length of rectangle = 12 ft

Weather affects flights across the nation, causing delays, cancellations, and general disruption to the NAS. You have gathered a random sample of departures delayed due to weather from your airport (KXYZ) for the month of April through July. You know that across America, weather delayed an average of 59 flights per day (σ =34.83) during that time period. You want to know if weather delays on flights from your airport differ significantly from those across the nation. Your significance level is set at 0.05. Analyze the data below using the correct t-test and be sure to check assumptions of the data.

Answer the following questions:

a. What type of t test should be used to address this research question, and why?
b. What is the null hypothesis?
c. What is the alternative hypothesis?
d. What is the mean and standard deviation for amount of the population?
e. What is the mean and standard deviation for the sample?
f. What are the degrees of freedom? How do you compute it?
g. What is the effect size (Cohen’s d) if applicable?
h. What is the test value?
i. What is the t statistic?

Answers

Answer:

a.) one sample t test

b.) H0 : μ = 59.3

c.) H1 : μ > 59.3

d.) μ = 59.3 ; σ = 39.84

e.) xbar = 79.4 ; s = 61.36

Test statistic = 3.16

Step-by-step explanation:

Given the sample data:

49.00 49.00 49.00 49.00 49.00 63.00 63.00 63.00 63.00 63.00 199.00 199.00 199.00 199.00 199.00 38.00 38.00 38.00 38.00 38.00 48.00 48.00 48.00 48.00 48.00 49.00 63.00 199.00 38.00 48.00

Sample size, n = 30

Using calculator :

xbar from the data above = 79.4

Standard deviation = 61.359

H0 : μ = 59.3

H1 : μ > 59.3

Test statistic :

(Xbar - μ) ÷ (σ/sqrt(n)

σ = 34.83

(79.4 - 59.3) ÷ (34.83/sqrt(30))

20.1 ÷ 6.359

Test statistic = 3.16

What is (8x + 4) added to (15x – 12)?

Answers

Answer:

23x-8

Step-by-step explanation:

8x + 15x = 23x

4 + (-12) = -8

Answer:

[tex] \boxed{23x \: – \: 8} [/tex]

Step-by-step explanation:

(8x + 4) added to (15x – 12) =

(8x + 4) + (15x – 12) =

[Group like terms]

(8x + 15x) + (4 – 12) =

[Simplify]

23x – 8

The diagram shows the spot on a basketball court called the "key". what is the area of the key? Use 3.14 for pi

Answers

3:1427726373owksisisieiieieir

PLEASE HELP !!!! ILL GIVE BRAINLIEST !!!

Answers

Answer:

Angle YXU is equal to 113 degrees. those are supplementary angles

Step-by-step explanation:

Respond to all of the questions within the topic (see that there are six questions below). 1. Explain how you can determine if the parabola opens up or down by simply examining the equation. 2. Give an example of a quadratic function with the given characteristics: its graph lies below the x-axis. 3. Explain how the number of solutions for a quadratic equation relates to the graph of the function. 4. Explain how you solve an equation by factoring. 5. In order to solve a quadratic equation by completing the square, what does the coefficient of the squared term need to be? If the coefficient is not equal to this, what does your first step need to be to complete the sqaure? 6. Explain how the discriminant can be used to determine the number of solutions a quadratic equation has.

Answers

Answer:

Step-by-step explanation:

Did you ever find the answer?/ I also am confused. please let me know

Can someone help me with this question please?

Answers

Answer:

35

Each sequence has a difference of eight numbers so we add 8 numbers in each sequence

Answer:

a) (i) 36

(ii) previous+8

b) 75

Step-by-step explanation:

a) (i) 27+8=36

(ii) previous+8

b) 10 th term is 3+9×8= 75

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