A certain length measurement is performed 500 times. The mean value is 5.0m, and the standard deviation is 2cms. Assuming a normal distribution for the error in the measurement, how many readings fall within 5.15cm of the mean value

Answers

Answer 1

Using the normal distribution, it is found that 495 readings fall within 5.15cm of the mean value.

In a normal distribution 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]

It 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, which is the percentile of X.

In this problem:

Mean of 5m, hence [tex]\mu = 5[/tex].Standard deviation of 2 cm, hence [tex]\sigma = 0.02[/tex]

To find the proportion of readings that fall within 5.15cm of the mean value, first we need to find the following z-score:

[tex]z = \frac{0.0515}{0.02}[/tex]

[tex]z = 2.575[/tex]

The proportion is P(|z| < 2.575), which is the p-value of z = 2.575 subtracted by the p-value of z = -2.575.

Looking at the z-table, z = -2.575 has a p-value of 0.005, and z = 2.575 has a p-value of 0.995.

0.995 - 0.05 = 0.99

Out of 500 measurements:

(0.99)500 = 495

495 readings fall within 5.15cm of the mean value.

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Related Questions

HELP ME OUT PLEASE!!!!!!!!

Which associations best describe the scatter plot?

Select each correct answer

Nonlinear association

Linear association

Negative association

Positive association​

Answers

Answer:

linear association, correct

Answer:

There are two answers: it is Nonlinear association and Linear association

Step-by-step explanation:

Nonlinear association- When comparing two data sets if the data from one set increase, the data from the second set decrease (it basically means a scatter plot that is decreasing).

Linear association- arranged in extending along a straight or nearly straight line.

I also took the test it it was correct.

From a large number of actuarial exam scores, a random sample of scores is selected, and it is found that of these are passing scores. Based on this sample, find a confidence interval for the proportion of all scores that are passing. Then find the lower limit and upper limit of the confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places.

Answers

Supposing 60 out of 100 scores are passing scores, the 95% confidence interval for the proportion of all scores that are passing is (0.5, 0.7).

The lower limit is 0.5.The upper limit is 0.7.

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].

60 out of 100 scores are passing scores, hence [tex]n = 100, \pi = \frac{60}{100} = 0.6[/tex]

95% confidence level

So [tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so [tex]z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6 - 1.96\sqrt{\frac{0.6(0.4)}{100}} = 0.5[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6 + 1.96\sqrt{\frac{0.6(0.4)}{100}} = 0.7[/tex]

The 95% confidence interval for the proportion of all scores that are passing is (0.5, 0.7).

The lower limit is 0.5.The upper limit is 0.7.

A similar problem is given at https://brainly.com/question/16807970

A coach divided his team into two groups of equal size.
.
of the first group drinks at least 2 glasses of water a day
• 75% of the second group drinks at least 2 glasses of water a day.
What fraction of the team drinks at least 2 glasses of water a day?

Answers

Applying the percentages, and considering that 70% of the first group drinks at least 2 glasses of water a day, it is found that 0.725 = 72.5% of the team drinks at least 2 glasses of water a day.

The team is divided into two equal groups, hence, each represents 50%.

The percentages associated with drinking at least 2 glasses of water a day is:

70% of 50%(first group)75% of 50%(second group)

Hence, applying the weighed percentage, the total percentage is:

[tex]T = 0.7(0.5) + 0.75(0.5) = 0.725[/tex]

0.725 = 72.5% of the team drinks at least 2 glasses of water a day.

A similar problem is given at https://brainly.com/question/1517088

What is 75.65 rounded to the nearest whole number?​

Answers

It is 76 as the other person said, what I like to think to help me remember is five or more raise the score, 4 or less, let it rest

Explain how you could solve the following using equal groups.

Linda wants to bake 48 cookies. The cookie tray has room for 8 cookies. How many batches will she have to bake to make 48 cookies?

Answers

Answer:

6

Step-by-step explanation:

48/8=6

Which of the following statements are true? Select all that apply.

Answers

explain better please?? Thanks

Answer:

They have 2 left one OR 2 right ones are true

Step-by-step explanation:

(X-2)(5x+6)

Multiply using Distributive property

Answers

[tex](x-2)(5x+6)\\\\=x(5x+6) -2(5x+6)\\\\= 5x^2 +6x -10x -12 \\\\=5x^2 -4x-12[/tex]

5x-10x+6x-12

-`9x-12

i believe so

A pair of sunglasses is on sale 30% off. if the original cost of the sunglasses are $18, what is the sale price now?

Answers

Answer:

12.60

Step-by-step explanation:

I don't feel like explaining it, since I'm not good at giving detail sorry <3

12.60 I hope this helps …………..

I NEED ANSWER NOW PLSSSSS​

Answers

Associate property because he was just rearranging the numbers using parentheses. Please mark me as brainiest!
Associative property

pls help, no false answer or link

Answers

Answer:

1. 10$

2. 24,59$

-1/3 + (-7/4)

Ill give this cookie to who solves it

Answers

Answer:

-25/12

Step-by-step explanation:

first, you need a common denominator. in this case, it's 12.

-1/3=-4/12

-7/4=-21/12

and then you add

-4+-21=-25

so -25/12 is your answer

......................................

can somebody help me with a tutor

Answers

Answer:

well tutors are very cool they help you with your subjects so i dont see any probelm with them.

Step-by-step explanation:

Yamuna is getting ready to attend Wittenberg University in the fall. She needs 6 notebooks
at $2.19 each and a chromebook at $529.00. If she has $575 to spend, how much does
she have left for lunch?

Answers

Answer:

she has $32.86 left for lunch

Step-by-step explanation:

6 books at $2.19 each equals $13.14. plus the chrome book at 529. 529+13.14= $542.14

$575-542.14 equals $32.86

When asked to factor the trinomial 8x^2-8x-16) a student gives the answer (X - 2)(x + 1). What is one thing wrong with this answer? - A. 8 is also a factor of this trinomial B. The minus sign should be a plus sign C. The factors are not simplified D. There is nothing wrong with the answer​

Answers

Answer:

8 is also a factor of this trinomial

Step-by-step explanation:

3/8 + 1/8 + 2/3 - 1/2 =

Answers

Answer: 2/3 (answer in decimal form = 0.6)

Step-by-step explanation: The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly. Then do the rest of the operations.

math models help PLEASE!

(20x5+10)-(8x8-4)



a . 58

b. 50

c. 40

Answers

Answer:

Answer is C, 40

Step-by-step explanation:

(100)-(60)

Find the product. Simplify your answer.
(3p–2)(4p–1)

Answers

there you go the answer is in the picture

с
6
D
15
8
B
?
А
1) Find the missing side length.
es
A) 14
B) 16
18
D) 20
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its
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3

Answers

Answer:

The answer would be 19

Step-by-step explanation:

Using pythagoras theorem

15+6= 21

a^2+b^2= c^2

In this scenario,

c^2-a^2= b^2

Meaning it would be 21^2+8^2

= 377

Square root of 377 would be 19.416

?= 19.416

The missing side length of the right angle triangle is 20

How to solve missing sides using Pythagoras theorem

Pythagoras theorem States that the square of the longest side of a triangle is equal to the sum of the square of the opposite side and no square of the adjacent side.

The diagram is a right angle triangle with sides AB, BC and CA.

The longest side is BC

BC² = AB² + CA²

(15 + 6)² = x² + 8²

21² = x² + 8²

21² - 8² = x²

441 - 64 = x²

377 = x²

find the square root of both sides

x = √377

x = 19.41648783894759891856148511263886343

Approximately to the nearest whole number

= 20

Learn more about Pythagoras theorem:

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You measure 43 randomly selected textbooks' weights, and find they have a mean weight of 75 ounces. Assume the population standard deviation is 12.4 ounces. Based on this, construct a 90% confidence interval for the true population mean textbook weight.

Answers

Answer:

by the empirical rule, 95% of the population is within 2 standard deviations of the mean

55 + or - 2(9.2) = 55+ or - 18.4 = (36.6,73.4)

95% of the population falls between 36.6 and 73.4 ounces

Step-by-step explanation:

Two hundred fifty tickets are sold at a fund raiser. If Sarah buys 15 tickets, the probability that she will win the prize quilt is
.

Answers

Answer:

6%

Step-by-step explanation:

15/250=3/50   or 6%

The probability that Sarah would win the prize quilt given the tickets she bought  is 6%.

What is the probability?

Probability is how likely it is that a stated event would happen. The probability of the event happening lie between 0 and 1.

The probability that Sarah would win the prize quilt = number of tickets bought / total number of tickets

(15 / 250) x 100 = 6%

To learn more about probability, please check: https://brainly.com/question/13234031

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[tex]{ \pink{ \displaystyle\tt \int_{0}^{1} \int_{0} ^{ x_{1}} } \sf \pink\int_{ 0 }^{x_{2}... \int_{ 0 }^{x_{99}}} ln(1 -x_{100} ) dx_{100}... dx_{1}}[/tex]
︎︎︎︎︎︎︎​

Answers

Step-by-step explanation:

[tex]\small{ \displaystyle\tt \int_{0}^{1} \int_{0} ^{ x_{1}} \int_{ 0 }^{x_{2}}... \int_{ 0 }^{x_{99}} ln(1 -x_{100} ) dx_{100}... dx_{1}}[/tex]

[tex]\small{{ \displaystyle\tt = - \int_{0}^{1} \int_{0} ^{ x_{1}} \int_{ 0 }^{x_{2}}... \int_{ 0 }^{x_{98}} \sum_{n = 1}^{ \infty \frac{}{} \frac{}{} } \frac{1}{n} \int_{0}^{x_{99}} {x}^{n}_{100} \: dx_{100}...dx_{1} }}[/tex]

[tex]{{ 0 }^{x_{98}} \frac{{x}^{n + 1}_{99}}{n + 1} \: dx_{99}...dx_{1} }[/tex]

[tex]\small{ \displaystyle\tt = -\sum_{n = 1}^{ \infty \frac{}{} \frac{}{} } \frac{1}{n}\int_{0}^{1} \int_{0} ^{ x_{1}} }[/tex]

[tex]\displaystyle \tt= - \frac{1}{(100)!_{} } \sum_{n = 1}^{ \infty } \frac{(n - 1)!(100)!}{(n + 101)!}=−(100)!1n=1∑∞(n+101)!(n−1)!(100)![/tex]

[tex]\displaystyle \tt= - \frac{1}{(100)!_{} } \sum_{n = 1}^{ \infty} \int_{0}^{1} {x}^{n - 1} (1 - x {)}^{100} [/tex]

[tex]\displaystyle \sf - \dfrac{1}{(100!)} \int_{0}^{1} \dfrac{(1 - x)^{100} }{1 - x} \:[/tex]

[tex]\displaystyle\tt { = - \frac{1}{(100)!} \int_{0}^{1} {x}^{99} \: dx=−(100)!1∫01x99dx}

[/tex]

Step-by-step explanation:

[tex]{ \pink{ \displaystyle\tt \int_{0}^{1} \int_{0} ^{ x_{1}} } \sf \pink\int_{ 0 }^{x_{2}... \int_{ 0 }^{x_{99}}} ln(1 -x_{100} ) dx_{100}... dx_{1}}[/t

︎︎︎︎︎︎︎

Goal 1000 points

What is 3/1,000 as a decimal

Answers

Answer: 3/1000 as a decimal is 0.003.

Explanation;

3/10 = 0.3

0.3/10 = 0.03

0.03/10 = 0.003

The correct answer to this question is 0.003.

What property is -5(-9x^2+8)+20=10x^2-15

Answers

Answer:

distributive?

Step-by-step explanation:

-5(-9x^2+8)+20=10x^2-15

simplify both sides

45x^2-20=10x^2-15

35x^2=5

x^2=1/7

x=1/sqrt(7)

distributive?

Choose which diagram

Answers

I assume it’s D but I’m not sure.
D because the lines match and all on how it mentions on the questions
Yeah it has to be D,hopefully it is

The value of the function f(x) = 5x +7 at 3 is

Answers

Answer:

22

Step-by-step explanation:

Substitute x = 3 into f(x) , that is

f(3) = 5(3) + 7 = 15 + 7 = 22

1. 6 km = ___ m
2. 8m = _____ km
3. 1dL = _____ mL
4. 30 kg = ____ g
5. 34 mg = ____ g.




!!!!!!! ​

Answers

6 km = 6000m8m = 0.008 km 1dL = 100 mL 30 kg = 30000g 34 mg = 0.034g.

Answer:

[tex]1)6000m \\ \\ 2)0.008km \\ \\\ 3)100ml \\ \ \\ 4)30000g \\ \\ 5)0.034g[/tex]

MARK ME AS A BRAINLIST PLZ

Six players compete in a tournament. Each player plays exactly two
games against every other player. In each game, the winning player
earns 2 points and the losing player earns 0 points. If the game results in
a draw (tie), each player earns 1 point. What is the minimum possible
number of points that a player needs to earn in order to guarantee that
he/she will be champion (i.e he/she has more points than every other
player)?

Answers

Step-by-step explanation:

6 players.

every player plays 2 games against every other player.

so, for each player there are 5 "other players" and everybody plays therefore 10 games.

the maximum number of points to get is 10×2 = 20 points.

the question is now not what is the minimum number of points a champion can have.

the question is rather what is the minimum number of points to guarantee the win of the championship no matter how the others played.

so, the study case scenario for the winner is to have only one real competitor for the title.

both players win every game against the other 4 players.

that is already 2×4×2 = 16 points.

and now it all depends on the 2 games against each other. to be sure, the winner needs at least 1 win and 1 tie in these 2 games. that are 3 more points.

so, to be absolutely sure, the champion needs to have at least 16+3 = 19 points.

The minimum possible number of points that a player needs to earn in order to guarantee that he/she will be champion 16+3 = 19 points.

What is unitary method?

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

Every player plays 2 games against every other player.

Then there will be 5 players left who will 10 games

So, the maximum number of points = 10*2 = 20

winning player earns 2 points

as, both players win every game against 4 players.

which gives = 2×4×2 = 16 points.

Now, in remaining two game the  winner needs at least 1 win and 1 tie

which needs 3 more points.

Hence, the minimum possible number of points that a player needs to earn in order to guarantee that he/she will be champion 16+3 = 19 points.

Learn more about unitary method here:

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Given: measure 1, measure 2, measure 3, and measure 4 formed by two intersecting segments Prove: measure 1 and measure 3 are congruent. NEED HELP ASAP!!​

Answers

Step-by-step explanation:

Note:

The text below that are formatted in bold and underlined font are the solutions to the missing boxes in your given problem.  

Explanation:

Given that ∠1, ∠2, ∠3, and ∠4 are formed by two intersecting segments, and that:

∠1 and  ∠2 form a linear pair  

∠2 and ∠3 form a linear pair  

These linear pair relationships suggest that by the Linear Pair Postulate:

∠1 and ∠2 are supplementary.    ⇒  Linear Pair Postulate

∠2 and ∠3 are supplementary.    ⇒  Linear Pair Postulate

m∠2 + m∠ 3 = 180°  ⇒  Definition of supplementary angles.

m∠1 + m∠3  = m∠2 + m∠ 3  ⇒  Substitution Property of Equality.          

m∠1  =  m∠3   ⇒  Subtraction Property of Equality.  

What is .7899 rounded 4 decimal places

Answers

.7899 rounded is .79. But in you want to convert/round it all the way it’s 1. But .79 makes more sense. Or .8. Which ever one works!!


Hope this helped. :)

A standard elevator in a midrise building can hold a maximum weight of about 1 3/4 tons. Assuming an average adult weight of 124 pounds, what is the maximum number of adults who can safely ride the elevator?

Answers

Answer: 28 adults

Step-by-step explanation: 1 3/4 tons is 3500 pounds which I divided by 124 pounds which gave me the answer 28

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