The amount of gasoline G sold each month to customers at Bob's Exxon station in downtown Navasota is a random variable. This random variable G can be described as having a normal distribution with mean 2500 gallons and a standard deviation of 250 gallons (and there is no seasonal variation in sales). Exxon will give Bob an all-expense paid trip to College Station, including a free dinner at Burger King, if his station pumps more than 3000 gallons in any one month.


Required:

What is the probability that Bob will win that wonderful trip on the basis of his gasoline sales this month?

Answers

Answer 1

Answer:

The probability is [tex]0.0228[/tex]

Step-by-step explanation:

Let's start by defining the random variable [tex]G[/tex] as :

[tex]G:[/tex] '' The amount of gasoline sold each month to customers at Bob's Exxon station in downtown Navasota ''

Therefore, if [tex]X[/tex] is a continuous random variable that has a normal distribution, we write [tex]X[/tex] ~ [tex]N[/tex] ( μ , σ )

Where ''μ'' is the mean and ''σ'' is the standard deviation.

For the random variable [tex]G[/tex] we write :

[tex]G[/tex] ~ [tex]N(2500,250)[/tex]

We need to find [tex]P(G>3000)[/tex]

In order to calculate this, we are going to standardize the variable. This means, finding the equivalent probability in a normal random variable

[tex]Z[/tex] ~ [tex]N(0,1)[/tex]

We perform this because the random variable [tex]Z[/tex] ~ [tex]N(0,1)[/tex] is tabulated in any book or either you can find the table on Internet.

To standardize the variable we need to subtract the mean and then divide by the standard deviation ⇒

[tex]P(G>3000)[/tex] ⇒ P[ (G - μ) / σ > [tex]\frac{3000-2500}{250}[/tex] ] ⇒ [tex]P(Z>2)[/tex]

Because (G - μ) / σ  ~ [tex]Z[/tex]

Finally, [tex]P(G>3000)=P(Z>2)[/tex] ⇒ [tex]P(Z>2)=1-P(Z\leq 2)[/tex] = 1 - Φ(2)

Where '' Ф(x) = [tex]P(X\leq x)[/tex] '' represents the cumulative function of [tex]Z[/tex]

Looking for  Φ(2) in any table,

[tex]P(G>3000)=P(Z>2)=1-P(Z\leq 2)=1-0.9772=0.0228[/tex] ≅ %2.28

We found out that the probability is [tex]0.0228[/tex]


Related Questions

When is the sum of two integers equal to zero? Explain.

Answers

Answer:

Rule: The sum of any integer and its opposite is equal to zero. Summary: Adding two positive integers always yields a positive sum; adding two negative integers always yields a negative sum. To find the sum of a positive and a negative integer, take the absolute value of each integer and then subtract these values.

Step-by-step explanation:

Hope this helped if so leave a rating! :)

THANKS!

can someone please help
f(t) = 2t - 3
f(7)=

Answers

11

explanation
2(7)-3=11

Can someone help me ASAP???

Four friends are in a swimming race. each Swim as many laps as they can and then tag the next one until they complete 50 laps the first swimmer completes 4/10 of the race. The 2ed completes 8 laps and the third summer complete 22% of the race how many laps will the last member have to swim to complete the race

Answers

Answer: The last member has to finish 11 more laps to complete 50 total laps

Step-by-step explanation:

[tex]\frac{4}{10}[/tex] of 50 =         20

2nd swimmer    8

22% of 50 =   + 11      

                        39 laps

---------------------------------------------

50 - 39 = 11 laps   (4th and last swimmer)

---------------------------------------------

P.S. I think this answer is late now

ABCD is a rectangle. The length of AC is 3x - 1. The length of BD is 2x + 5.
What is the length of AC?
a.3
b.6
c.13
d.17

Answers

Answer:

C.13

Step-by-step explanation:

3x - 17 = 2x + 35
Please help

Answers

Answer:

[tex]x = 52[/tex]

Step-by-step explanation:

We have the following equation:

[tex]3x -17=2x+35[/tex]

First we simplify the numbers.

[tex]3x -17+17=2x+35+17[/tex]

[tex]3x=2x+52[/tex]

[tex]3x-2x=2x-2x+52[/tex]

[tex]x=52[/tex]

Answer:

x = 52

General Formulas and Concepts:

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define equation

3x - 17 = 2x + 35

Step 2: Solve for x

Subtract 2x on both sides:                           x - 17 = 35Add 17 to both sides:                                    x = 52

Step 3: Check

Plug in x to verify it's a solution.

Substitute:                         3(52) - 17 = 2(52) + 35Multiply:                             156 - 17 = 104 + 35Subtract/Add:                    139 = 139

What is the value of the expression -6 3/4 -1 3/12

Answers

Answer:

-8

Step-by-step explanation:

Which expression is equivalent to -51-(-60)

Answers

Answer:

-51 + 60

Step-by-step explanation:

When subtracting with negative numbers use the "keep, change opposite" skill. Keep your first number which in this case, is -51, then change the subtraction sign to addition and lastly change the sign of your last digit which is (-60) so opposite of that just 60.

(Giving brainliest!!!)

How do you solve 7,124 ÷ 26 using standard algorithm?

Answers

Answer:

274

Step-by-step explanation:

The standard algorithm of multiplication is based on the principle that you already know: multiplying in parts (partial products): simply multiply ones and tens separately, and add.

However, in the standard way the adding is done at the same time as multiplying. The calculation looks more compact and takes less space than the “easy way to multiply” you have learned.(i really think this is correct but I am so so sooo sorry if it's not!!!!)

What does this equal too(2x-5)^2

Answers

Answer:

4x² - 20x + 25

Step-by-step explanation:

(2x-5)² means (2x-5)(2x-5)

Expand the brackets.

1. do 2x times 2x = 4x²

2. do 2x times -5 = -10x

3. -5 times 2x = -10x

4. -5 times -5 = 25

Altogether it is 4x² - 10x - 10x + 25

This simplifies to 4x² -20x + 25.

Use the digit 5, 7, and 2 to write four numbers that are greater than 400.​

Answers

Answer:

All the possible numbers:

257275527572725752

numbers greater than 400:

527572725752

your answers : 527, 572, 725, 752

mrk as brainleist ☺️

Use proportions to solve. A person is standing near a tree. The person is 5 feet tall and casts a shadow that is 3 feet long. The tree casts a shadow that is 7 feet long.Use proportions to solve. A person is standing near a tree. The person is 5 feet tall and casts a shadow that is 3 feet long. The tree casts a shadow that is 7 feet long.

Answers

Answer:

d

Step-by-step explanation:

make me brainelist

The proof that HG ≅ EG is shown.

Given: G is the midpoint of KF

KH ∥ EF

Prove: HG ≅ EG

Triangles F E G and K H G are connected at point G.

What is the missing reason in the proof?

Statement
Reason
1. ∠EGF ≅ ∠HGK 1. vert. ∠s are ≅
2. KH ∥ EF 2. given
3. ∠F ≅ ∠K 3. alt. int. ∠s are ≅
4. G is the midpoint of KF 4. given
5. FG ≅ KG 5. def. of midpt.
6. △FEG ≅ △KHG 6. ?
7. HG ≅ EG 7. CPCTC
SAS
ASA
AAS
HL

Answers

Answer:

ASA

Step-by-step explanation:

The Proof proves that two of the angles and the included side are equal making it the ASA theorem

The missing reason in the given proof is ASA.

What is Congruence of Triangles?

Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.

Given is a proof for the congruence of the lines HG and EG.

Given,

G is the midpoint of KF.

KH ∥ EF

Triangles F E G and K H G are connected at point G.

We have to prove HG ≅ EG.

From the given steps of proof,

we get two angles and the included side of triangle FEG is congruent to corresponding two angles and the included side of triangle KHG.

So by ASA theorem both triangles are congruent.

Hence the missing reason is ASA.

Learn more about Congruence Rules here :

https://brainly.com/question/20521780

#SPJ7

Use substitution to solve the system.
x = 3y - 12
5x + 3y = 30
I would appreciate answers

Answers

Answer:

its ( 3,5) Equation form is: x  =  3  ,  y  =  5

Step-by-step explanation:

What is 24×4
please answer and give expalnation

Answers

(1)24
4*
___
96
0+
____
96
(4*4)=16 = 6 (the 6 will remian and one we added with 2)
(2+1*4)=9
know the answer will be 96

HURRY PLEASE!!! I NEED TO TURN THIS IS SOON!! I WILL GIVE YOU BRAINLIEST!!
i need the equation you solved it with also!

Answers

Answer:

x=31

Step-by-step explanation:

180-75=115

4x-9=115

4x=124

x=31

i need some help with this ​

Answers

I think it’s b or c.

HELP ME PLSSS Which of the following number sentences is an example of the associative property of multiplication?
O (12 * 3) 8 = 12 (3 x 8)
6x1 = 6
4* 5 = 5 x4
20 * (10 + 6) = (20 x 10) + (20 * 6)

Answers

Answer:

The first or third one

Step-by-step explanation:

Associative property is where you can switch the place of the digits and it still have the same answer in the end.

A community hall is shape of a cuboid. The hall is 40 m long, 15 m wide and 3 m high. The community hall needs re-decorating with new point for the walls and ceiling, and new tiles on the floor. A 10 litre tin of paint covers 25m*25m and costs £10. 1m*1m floor tiles cost £3 each. Work out the total cost of paint and tiles needed to re-decorate the community hall.

Answers

Total cost for tiles and paints is $924.
Step-by-step explanation:
We have been given that a community hall is in the shape of a cuboid. The hall is 40m long 15m high and 3m wide.
The paint will be required for 4 walls and ceiling.
Let us find area of walls and ceiling.



Therefore, the area of walls and ceiling is 1410 square meters.
Given: Cost for 10 litre of paint is $10 and 10 litre paint covers 25 square meter. Therefore,


Therefore, the total painting cost is $564.
Tiles will be required for floor. Let us find the area of floor.


Given: 1m squared floor tiles costs $3. So,

Therefore, the total cost for tiles is $360.
Now let us find combined total cost of tiles and paint.

Therefore, the combined total cost of tiles and paint is $924.

if Afsheen can read 39 pages of a book in half an hour how much will it take her to finish the book that is 1287 pages​

Answers

We are given:

Afsheen can read 39 pages in 30 minutes

Time taken by Afsheen to read 1287 pages:

Time taken to read 1 page:

Time taken to read 1 page = time taken to read 39 pages / 39

Time taken to read 1 page = 30 minutes / 39

Time taken to read 1 page = 0.77 minutes

Time taken to read 1287 pages:

Time taken to read 1287 pages = Time taken to read 1 page * 1287

Time taken to read 1287 pages = 0.77 * 1287

Time taken to read 1287 pages = 991 minutes OR 16.52 hours (Approx)

Answer:

in 1 hour = 2×39= 78 pages

so 1287 pages= 1287÷78= 16.5 hours

Step-by-step explanation:

it takes 16. 5 hours that means 16 hours 30 min

answer thisss please​

Answers

Answer:

Real numbers: Tick all of the numbers

Rational numbers: Tick all except 3.55687143...

Irrational numbers: Tick 3.55687143...

Integers: Tick 7 and -18

Whole number: Tick 7

Step-by-step explanation:

Real numbers are basically any number.

Rational numbers are numvers which can be converted into a fraction.

Irrational numbers are numbers which cannot be converted into a fraction.

Integers are whole numbers including negative numbers.

Whole numbers are the same as integers but do not include negative numbers.

7 comedy dvds, 4 more drama dvds than horror dvds. 15 dvds in all. how many drama and horror dvds are there?​

Answers

Step-by-step explanation:

2 horror and 6 drama DVDs.

Let x be the no. Of horror dvds

15 = 7+ x+x+4

4=2x

x=2

What is the atomic number of an atom?


A. the number of electrons and neutrons


B. the number of protons


C. the number protons and neutrons


D. the number of neutrons

Answers

Answer:

the number of protons in the nuclues of an atom

2-(-8)+(-3)= I just need the answer not the work

Answers

Answer:

7

Step-by-step explanation:

:)

Write two equivalent ratios for 8 and 9

Answers

Answer:

16:18

24:27

Step-by-step explanation:

16:18 ( multiply both numbers by 2)

24:27 ( multiply both numbers by 3)

Hope this helped even tho I am late

what linear function contain the following point (-4, 4) and (0, 5)

Answers

Answer:

y = 1/4x + 5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Slope-Intercept Form: y = mx + b

m - slope b - y-intercept

Step-by-step explanation:

Step 1: Define

Random Point (-4, 4)

y-intercept (0, 5)

Step 2: Find slope m

Substitute:                    [tex]m=\frac{5-4}{0+4}[/tex]Subtract/Add:               [tex]m=\frac{1}{4}[/tex]

Step 3: Write linear equation

y = 1/4x + 5

Kevin plants a total of 72 flower in equal rows. He plants 6 rows of of yellow flowers and 2 rows of red flowers. How any flowers are in each row?

Answers

Answer: 36

Step-by-step explanation: 72/6= 36

72/2= 37

4x-3(x+4)=7 i need to know this i need help with this.

Answers

Answer:

x=19

Step-by-step explanation:

4x-3x-12=7

x-12=7

x=7+12

x=19

Answer:

x=19

Step-by-step explanation:

first you would distribute the -3 to the x and the 4 which would give you

4x-3x-12=7

next you would combine like terms (there's always an invisible 1 one front of a variable)

x-12=7

then to get the variable by itself you would add 12 on each side

x=19

hope this helped :)

HELP ME OUT REAL QUICKKKKKKKKKKKKK

Answers

The answer should be 7/8
The answer is b 7/8 good luck

PLEASE HELP QUICK WILL GIVE BRAINLIEST
What is the new equation if the parent function, y = 2*, is reflected over the
asymptote, and vertically shifted 8 units up?

Answers

f(x)=ex f ( x ) = e, x is vertically stretched by a factor of 2. Hope this helps!

What is the value of P(S and T)?

A.

B.

C.

D

Answers

Answer:

0.25 but I am not sure umm I think

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