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

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

Answers

Answer:

Step-by-step explanation:

(Decimal: 1.222222)

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

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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:

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Answers

Answer:

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Step-by-step explanation:

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

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Step-by-step explanation:

What is the slope of a line passing
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Answers

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-4/3

Step-by-step explanation:

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when you do the calculations you get -4/3

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

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.

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Just take a look at it.

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Answer:

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Step-by-step explanation:

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
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Answers

Answer:

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Step-by-step explanation:

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

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

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

Sorry

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Answers

Answer:

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Answer:

18

Step-by-step explanation:

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

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= 16+8(4⁻¹)

=16 + 8(1/4)

=16+2

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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:

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Answers

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Step-by-step explanation:

s

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Answers

Answer:

49, 35, 32

Step-by-step explanation:

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

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

Or it’s only factors are 1 and itself

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Answer: 49,32,35.

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Answer:

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Step-by-step explanation:

Answer:

aaaaaaaaa

Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer:

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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

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nothing nothing nothing nothing

Step-by-step explanation:

nothing nothing nothing nothing nothing nothing nothing nothing

stream positons by ariana grande <3

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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.

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89
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.

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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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.

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