CNNBC recently reported that the mean annual cost of auto insurance is 965 dollars. Assume the standard deviation is 113 dollars. You will use a simple random sample of 57 auto insurance policies.Find the probability that a single randomly selected policy has a mean value between 939.6 and 972.5 dollars.P(939.6 < X < 972.5)

Answers

Answer 1

Answer:

P(939.6 < X < 972.5) = 0.6469

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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 zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

CNNBC recently reported that the mean annual cost of auto insurance is 965 dollars. Assume the standard deviation is 113 dollars.

This means that [tex]\mu = 965, \sigma = 113[/tex]

Sample of 57:

This means that [tex]n = 57, s = \frac{113}{\sqrt{57}} = 14.97[/tex]

Find the probability that a single randomly selected policy has a mean value between 939.6 and 972.5 dollars.

This is the pvalue of Z when X = 972.5 subtracted by the pvalue of Z when X = 939.6. So

X = 972.5

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

By the Central Limit Theorem

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

[tex]Z = \frac{972.5 - 965}{14.97}[/tex]

[tex]Z = 0.5[/tex]

[tex]Z = 0.5[/tex] has a pvalue of 0.6915

X = 939.6

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

[tex]Z = \frac{939.6 - 965}{14.97}[/tex]

[tex]Z = -1.7[/tex]

[tex]Z = -1.7[/tex] has a pvalue of 0.0446

0.6915 - 0.0446 = 0.6469

So

P(939.6 < X < 972.5) = 0.6469


Related Questions

A horse has a water barrel in which 3/10 of a gallon is drank out of it every day. How many days will it take the horse to drink 42 gallons of water?

Answers

Answer:

140 days

Step-by-step explanation:

140 days


Explanation:

3/10 x 42 would be 40 then times it by 100 to get 140, hope this helps :)

In a population of 2000 students, 230 are left-handed. A random sample of size
50 is selected and the number of left-handed students is recorded. If we
collected many more samples, which of the following could describe the
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Answers

11.5% is the correct answer

HELP ME!!!! PLZ!!!!

The determinants of the minors of the first-row entries are _____ .
11, -20, 23
11, -16, 26
13, -20, 23
13, -16, 26
The determinants of the minors of the second-row entries are______ .
-21, 5, -24
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Answers

Answer:

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A sum of money was divided bety
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he money and Dónal got the res
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Answers

Answer:

4.00

Step-by-step explanation:

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Answers

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Step-by-step explanation:

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500 is what percent of 125?​

Answers

400% is because 125 divided by 500 is 400

Answer:

400

Step-by-step explanation:

Solution for 500 is what percent of 125:

500:125*100 =  

(500*100):125 =  

50000:125 = 400  

Now we have: 500 is what percent of 125 = 400  

Question: 500 is what percent of 125?  

Percentage solution with steps:  

Step 1: We make the assumption that 125 is 100% since it is our output value.  

Step 2: We next represent the value we seek with [tex]x%[/tex].  

Step 3: From step 1, it follows that $100%=125$.

Step 4: In the same vein, $x%=500$.

Step 5: This gives us a pair of simple equations:

100%=125(1)

x%=500(2)

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS

(left-hand side) of both equations have the same unit (%); we have

[tex]\frac{100\%}{x\%}=\frac{125}{500}[/tex]

Step 7: Taking the inverse (or reciprocal) of both sides yields

[tex]\frac{x\%}{100\%}=\frac{500}{125}[/tex]

[tex]\Rightarrow x=400\%[/tex]

Therefore, 500 is 400% of 125

Hope this answer helps and answers your question! Have a great day/night!

Kristin has 3 2/3 yards of plaid ribbon. She has 2 5/6 yards of polka-dot ribbon.

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Answers

Answer:

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Step-by-step explanation:

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Answer:

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2 is 14.2

Step-by-step explanation:

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Answers

Answer:

Step-by-step explanation:

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Eight bricks are laid end to end along the edge of a flower bed. Each brick is inches long. How long is the row of bricks, in inches?

Answers

Eight bricks are laid end to end along the edge of a flower bed.

Each brick is 11/2 inches long. How long is the row of bricks, in inches?

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Answer:

1.5 times 8 equals 12. The row of bricks is 12 inches long

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Answers

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Answer:

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Use a calculator (;

1) (35 + 17) + 43 = 35+ (17 + 43)

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Answer:

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Step-by-step explanation:

what is the relationship between a magnets magnetic force and magnetic field?​

Answers

Answer: They both use a magnetic pull?

Step-by-step explanation:

A={0 ; 4 ; 1 supra 3 ; -5 ; 0,(4) ; -2 ; 8 supra 4}
a) A ( U intors ) N ( multimea numerelor naturale )
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A? I don’t understand

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Chu gf fr uvv V dhh gg jb cub

What is the equation for the line of reflection?
ФУ
4
B
B
A
A'
2
D
с
C
D'
Х
2
6
8
10
27

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Answer:

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Step-by-step explanation:

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Answers

Answer:

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Answers

Answer:

Step-by-step explanation:

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Answer:

Step-by-step explanation:

The key word is increase.

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Answers

Answer:

Lily: 12(C + L) + 35

Step-by-step explanation:

Variables:  C (Carlos) and L (Lily)

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We do not know how long they worked

We do know Carlos got an extra $35.

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12(C + L)+35

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1 A lawnmower that regularly sells for $200 is on sale for $85. Find the % of change that the price was decreased by ??? percent. Round to the nearest whole percent.

Answers

Answer:

The price changed by 92.5 %

Step-by-step explanation:

The regular price of lawn mover = 200 dollars

The new selling price = 85 dollars

Change in selling price = 200 -85 dollars = 115 dollars

% change == [tex]\frac{185}{200} * 100 = 92.5[/tex]

The price changed by 92.5 %

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Answers

Answer:

P + 1/4 (is greater than or equal to) 2

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Step-by-step explanation:

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Answers

Answer:

The good kind

Step-by-step explanation:

Yes

Answer:

15n+19.95=c

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Answers

Answer:

Assuming that "x" symbol indicates multiplication, the answer should be 4/3. If you need the decimal form, it would be 1.3. If you want the mixed number form, it'd be 1 1/3.

Step-by-step explanation:

4/5x 1 2/3

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12/3 in decimal is 4

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Answers

Answer:

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Step-by-step explanation:

-4x4x(-3x2+9)=-48

Answer:

12x^7−36x^5

Step-by-step explanation:

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Answers

Answer:

26

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Answers

Answer:

Step-by-step explanation:

Does log7(x^5+x) mean log₇(x⁵+x) ?

The population of the UK is 64 million compared to the world's population of 7 billion (7000 million).

Write this proportion as a percentage, correct to 1 decimal place.

Answers

Answer:

0.009%

Step-by-step explanation:

64/7000*100=0.009142857%

The proportion of population in UK to the world population is 64 : 7000 or

0.9 %

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

Given data ,

Let the value of population in UK be = 64 milliom

Let the value of world population be = 7 billion

Now ,

The value of 1 billion = 1000 million

So , the value of 7 billion = 7 x 1000 million

The value of 7 billion = 7000 million

Now , the value of world population is = 7000 million

So , the proportion of population of UK to the world population is given by = value of population in UK : value of world population

And , the equation will be

The proportion of population of UK to the world population is = 64 : 7000

The proportion of population of UK to the world population is = 0.00914

The proportion of population of UK to the world population is = 0.9 %

Hence , The proportion of population in UK to the world population is

64 : 7000 or 0.9 %

To learn more about proportion click :

https://brainly.com/question/7096655

#SPJ2

A1 kg object is located at a distance of 6.4 x10^6 m from the center of a larger object whose mass is 6.0 x 10^24 kg. Find the gravitational attraction between them. *
O 11 N
O 8 N
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O 6.8 N​

Answers

Answer:its 11n

Step-by-step explanation:

Simple divide all

The gravitational attraction between the two objects as described is; 9.77N

The force of gravitational attraction according to Newton's law of gravitation can be expressed mathematically as;

F = G m1m2/r²

where F = force of attractionG = gravitational constant = 6.67 × 10-¹¹ m3 kg-¹ s-²m1 and m2 = mass of the objects respectivelyr = their distance apart.

F = (6.67 × 10-¹¹ × 1 × 6.0 x 10²⁴)/(6.4 x 10⁶)²

F = 9.77 N

Read more:

https://brainly.com/question/9663501

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