The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 4959 miles, with a standard deviation of 448.If he is correct, what is the probability that the mean of a sample of 43 cars would differ from the population mean by less than111 miles? Round your answer to four decimal places.

Answers

Answer 1

Answer:

0.8958

Step-by-step explanation:

Given that:

The mean [tex]\mu[/tex] = 4959

The standard deviation [tex]\sigma[/tex] = 448

The sample size n = 43

[tex]\mu_{\overline x} = \mu = 4959[/tex]

[tex]\sigma __{\overline x}} = \dfrac{\sigma}{\sqrt{n}}= \dfrac{448}{\sqrt{43}}[/tex]

By applying the central limit theorem;

[tex]\overline X \sim N \bigg( \mu_{\overline x} = 4959 , \sigma_{\overline x} = \dfrac{448}{\sqrt{43}}\bigg )[/tex]

The purpose of this question is to calculate the probability that the mean of a sample of 43 cars would differ from the population mean by less than111 miles.

This implies that;

[tex]P( |\mu-\overline x| <111) = p( 4959-111 < \overline X < 4959 +111)[/tex]

[tex]= P( 4848 < \overline X < 5070)[/tex]

[tex]= P \bigg ( \dfrac{ \overline x - \mu_x }{ \dfrac{\sigma}{\sqrt{n}}} < Z < \dfrac{ \overline x - \mu_x }{ \dfrac{\sigma}{\sqrt{n}}} \bigg )[/tex]

[tex]= P \bigg ( \dfrac{4848 -4959 }{ \dfrac{448}{\sqrt{43}}} < Z < \dfrac{5070 -4959 }{ \dfrac{448}{\sqrt{43}}} \bigg )[/tex]

[tex]= P \bigg ( \dfrac{-111 }{ 68.319} < Z < \dfrac{111 }{68.319} \bigg )[/tex]

[tex]= P ( -1.6247< Z < 1.6247 )[/tex]

= P ( Z < 1.627 ) - P(Z < -1.627)

From the standard normal tables

= 0.94791 -0.05208

= 0.89583

0.8958  to four decimal places.


Related Questions

if the number of different schedules is represented by three consecutive even integers, what is the expression for that total number of schedules they have to choose from?

Answers

Answer:

s

Step-by-step explanation:

s

=3x+6

Apply the distributive property x+( x+2)+(x+4)
Arrange like terms = x+x+2+x+4
Simplify =x+x+x+2+4
=3x+6

1. If OQ and RT are parallel lines which statement is true?

A) OPS is congruent to RSU

B) OPS is congruent to RSP (my answer)

C) OPS is congruent to OPN

D) OPS is congruent to TSU

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

2. If OQ and RT are parallel lines which statement is true?

A) RSP is congruent to RSU

B) RSP is congruent to PST

C) RSP is congruent to TSU

D) RSP is congruent to OPS (my answer)

Answers

Answer:

Step-by-step explanation:

Question (1).

OQ and RT are the parallel lines and UN is a transversal intersecting these lines at two different points P and S.

A). ∠OPS ≅ ∠RSU [corresponding angles]

B). m∠OPS + m∠RSP = 180° [Consecutive interior angles]

C). m∠OPS + m∠OPN = 180° [Linear pair of angles]

D). Since, ∠OPS ≅ ∠TSP [Alternate interior angles]

    And m∠TSP + m∠TSU = 180° [Linear pair of angles]

Therefore, Option (A) is the correct option.

Question (2).

A). m∠RSP + m∠RSU = 180° [Linear pair of angles]

B). m∠RSP + m∠PST = 180° [Linear pair of angles]

C). ∠RSP ≅ ∠TSU [Vertically opposite angles]

D). m∠RSP + m∠OPS = 180° [Consecutive interior angles]

Therefore, Option (C) will be the answer.

Answer:

C

Step-by-step explanation:

OQ and RT are parallel lines, while UN is a transversal that crosses both lines at two points. P and S are a couple.

A). RSU [corresponding angles] OPS

B). [Consecutive interior angles] mOPS + mRSP = 180°

C). [Linear pair of angles] mOPS + mOPN = 180°

D.) Since then, OPS TSP [Alternate Interior Angles] has been implemented.

And [Linear pair of angles] mTSP + mTSU = 180°

As a result, Option (A) is the right one.

Inquiry (2).

A). [Linear pair of angles] mRSP + mRSU = 180°

B). [Linear pair of angles] mRSP + mPST = 180°

C). [Vertically opposite angles] RSP TSU

D). [Consecutive interior angles] mRSP + mOPS = 180°

so it’s gonna have to be C

Ina crespo rowed 7.5 miles down the Hanbashabee river in 1.5 hours ,but the return trip took her 2.5 hours.find the rate ina rows in still water and the rate of the current.

Answers

Answer:

rate of current=1 mph

Step-by-step explanation:

carpenter charges $45 for every 50 feet of fence he builds plus a travel charge of $37.50.

Answers

Answer:

350 feet

Step-by-step explanation:

352.50 - 37.50= 315

315 ÷ 45 = 7

7 × 50 = 350

The three perpendicular bisectors of the sides of AABC intersect at point G. Point G is the
A)
centroid.
B)
circumcenter.
C)
incenter:
D)
orthocenter.

Answers

Answer: B) Circumcenter

Answer: Circumcenter

Step-by-step explanation:

Please view the photo below for proof that it is accurate.

Mr. Wong was born in 1934. In what year was Mr. Wong 48 years old?

Answers

Answer:

1886 i think thats right if you do the math

Step-by-step explanation:

Please help fast!! Is this a function?

Answers

Answer:

It's not a function..

Step-by-step explanation:

Just take a look at it.

what did u studied about functions before doing this type of problem in math?

Does it look like it? no.

Answer:

That looks very hard .. sorry :(

Step-by-step explanation:

which number are composite numbers-49,35,32,41,47

Answers

Answer:

49, 35, 32

Step-by-step explanation:

A prime number is a number whose factors are 1 and itself

Eg 7

7 is a prime number because it only comes in table one and 7

Or it’s only factors are 1 and itself

A composite number comes in 1, itself and other tables

Eg. 16

It comes in table 1, 2, 4 and 16

Answer: 49,32,35.

Hope this helps!

What is 2÷1/7 equal to
A 14
B 7
C 7/2
D 15/7
E 2/7

Answers

Answer:

14! So a

Step-by-step explanation:

Answer:

aaaaaaaaa

Step-by-step explanation:

aaaaaaaaaaaaaaaa

there is only three options someone help

Answers

Answer:

Answer is Option 2

Step-by-step explanation:

Triangles equal to 180 degrees in total. So it is 55+54+x+74=180

The simplified version that I just wrote is Option 2

will give brainliest!!!! The value of the 5 in the number 594,631 is how many times larger than the value of the 5 in the number 859,463? *

Answers

Answer:

It's 10 times larger.

Step-by-step explanation:

If you just have 500,000, and the other one is 50,000, That means 50,000 x 10 is 500,000.

please help need assistance

Answers

Answer:

18

Step-by-step explanation:

Keep in mind that anything with a subscript of 0 always comes out as a 1

16(1)+2(2)²(4⁻¹)

= 16+8(4⁻¹)

=16 + 8(1/4)

=16+2

=18

Hope this helps! :)

what is the factored form of x^-9

Answers

Answer:

1/x^9

Step-by-step explanation:

I don't actually understand this question, but if you are asking (x^(-9)), then its the answer above

sergio must ride 7.5 miles in 1/4 hour to achieve this target speed, so he needs to ride an additional ____ mile per 1/4 hour

Answers

Answer: 7.0

Step-by-step explanation:

sergio must ride 7.5 miles in 1/4 hour to achieve this target speed so  he needs to ride  an addititonal 9.8 mile per1/4 hour

Answer:

30 mph

Step-by-step explanation:

since it is 1/4  you would multply 7.5 times 4, which adds up to 30.

Solve five ninths plus four sixths. Answer this and ill give brainliest

Answers

Answer:

Step-by-step explanation:

(Decimal: 1.222222)

Sally’s Rent-A-Bike store rented 200 bicycles in June. In July, the store rented 300 bicycles. What percent of the bicycles rented in June were rented in July?

Answers

Answer:The answer is 150%

Step-by-step explanation:

I just did this and got it correct:)Trust me this is correct!!

Answer:

150%

Step-by-step explanation:

nothing nothing nothing nothing

Answers

Answer:

nothing nothing nothing nothing

Step-by-step explanation:

nothing nothing nothing nothing nothing nothing nothing nothing

stream positons by ariana grande <3

What expression represents the decimal 72.603?

7 x 10 + 2 x 1 + 6 x 1/100 + 3 x 1/1000
7 x 1 + 2 x 10 + 6 x 1/10 + 3 x 1/100
7 x 10 + 2 x 1 + 6 x 1/10+ 3 x 1/1000
7 x 1 + 2 x 1 + 6 x 1/10+ 3 x 1/100

Answers

Answer:

C or  7 x 10 + 2 x 1 + 6 x 1/10+ 3 x 1/1000

Step-by-step explanation: just had this on the test

The correct expression for the expansion of 72.603 is 7 x 10 + 2 x 1 + 6 x 1/10 + 3 x 1/1000 (option 3rd)

What is an expression?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is a decimal number, 72.603

On expanding it, we get,

72.603 = 72 + 0.603

= 7 x 10 + 2 x 1 + 6 x 1/10 + 3 x 1/1000

Hence, the correct expression for the expansion of 72.603 is 7 x 10 + 2 x 1 + 6 x 1/10 + 3 x 1/1000

Learn more about expressions, click;

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Question: Using only reciprocal, Pythagorean, sum/difference, and/or half angle identities, prove the equation below. You must use angles A and B, do not replace with actual vales. Only work with the right side of the equation. You should use TEN steps to accomplish this proof! cosA+cosB= 2cos(A+B/2)cos(A-B/2)​

Answers

Answer:

See explanation below

Step-by-step explanation:

Recall the identity for the cosine of an addition of angles:

[tex]cos(\theta+\gamma)= cos(\theta)*cos(\gamma)- sin(\theta)*sin(\gamma)[/tex]

and that for a subtraction of angles:

[tex]cos(\theta-\gamma)= cos(\theta)*cos(\gamma)+sin(\theta)*sin(\gamma)[/tex]

Now, use the property of addition of angles above to write :

[tex]cos(\frac{A+B}{2} +\frac{A-B}{2} )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )-sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )[/tex]

but since :  [tex]\frac{A+B}{2} +\frac{A-B}{2}= A[/tex]

Then the cosine of addition of angles above can be written as:

[tex]cos(\frac{A+B}{2} +\frac{A-B}{2} )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )-sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )\\cos(A)=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )-sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )[/tex]

We do something similar now with the cosine of the subtraction of angles:

[tex]cos(\frac{A+B}{2} -\frac{A-B}{2} )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )+sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )[/tex]

and we notice that: [tex]\frac{A+B}{2} -\frac{A-B}{2}= B[/tex]

Then the cosine of subtraction of angles above can be written as:

[tex]cos(\frac{A+B}{2} -\frac{A-B}{2} )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )+sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )\\cos(B )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )+sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )[/tex]

and finally, we add term by term the expressions we got for cos (A) and for cos(B) and notice that the terms that contain the sine functions cancel each other because they have opposite signs, while the terms in cosine add up to double themselves:

[tex]cos(A )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )+sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )\\+\\cos(B )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )-sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )\\=\\cos(A) +cos(B)=2\,cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )[/tex]

which is what we wanted to prove.

Replace the a , b , c , and d with the dighits 2,4,6,8 to form the greatest product. Each digit can only be used once. Explain your substitutions.

a0b
x c d
--------------------------

Answers

Answer:

2x4x6x8

Step-by-step explanation:

each one can only be used once so its only possible for 2x4x6x8

Determine if each line is proportional non-proportional or non-liner

Answers

Step-by-step explanation:

non-proportiona

What is 2.18-0.3? Feel free to answer

Answers

Answer:

the answer for this is 1.88 u just subtract

Find the value of a and b in the following = a + b​

Answers

what is the question??

To find the quotient of 4 divided by 1/5 multuply 4 by

Answers

Multiply 4 by 5
5 is the answer

Answer:

There is not enough information for me to solve what you want solved.

Step-by-step explanation:

Sorry

Which table shows a proportional relationship between weight and price?
Price
Weight
Price
Weight
1.5 lb
$3.50
1.5 g
$0.90
8
2 lb
$7.00
89
$4.80
Price
Weight
Price
Weight
2 kg
$0.75
2 oz
$4.00
5 kg
$3.75
4 lb
$8.00
.

Answers

I also think c !!!!!!

Table 4 is showing proportional relationship between weight and price.

What is proportionality?

The number or amount of a group or part of something when compared to the whole, is considered as proportionality.

Given that, a table of proportional relationship between weight and price;

If we consider table number 4,

We see, weight : price = 2 : 4 = 1 : 2

And, 4 : 8 = 1 : 2

Therefore, this is showing proportionality,

Hence, Table 4 is showing proportional relationship between weight and price.

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Captain America's circular shield has a diameter of 76.2 centimetres. What is the area of his shield?

Answers

Answer:

Its area is 370 square centimeters.

Step-by-step explanation:

is 3 months enough time to complete 300 assignments? my school is online and requires you to complete a certain amount of assignments each semester.

Answers

Answer:

ya if you do 3 a day

Step-by-step explanation:

Answer:

yes it is enough time you would have to do 25 assignments aweek

Step-by-step explanation:

What is the slope of a line passing
through points (-6, 3) and (-3, -1)?

Answers

Answer:

-4/3

Step-by-step explanation:

you do change in y over change in x which is -1-3 over -3-(-6)

when you do the calculations you get -4/3

The radius of the circle is 13 what’s the diameter

Answers

Answer:

d = 26

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Geometry

Diameter: d = 2r

Step-by-step explanation:

Step 1: Define

Radius r = 13

Step 2: Find diameter

Substitute:                    d = 2(13)Multiply:                        d = 26

for the below question assume no duplicated units are allowed all the answers for a 5 question multiple choice test are a b c d find the number of possible answer keys a teacher could have

Answers

Answer:

4

Step-by-step explanation:

1 2 3 4 so 4 because 4 is the last number before 5

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