Mathematics, 16.02.2021 04:30 ashtonbillups

You are designing an automatic coin counter that stacks 50 pennies at a time to be placed in coin wrappers. You plan on measuring the height of the stack to determine the number of coins, but are concerned as to how accurate the method will be. You measure the thickness of 30 pennies, with the data listed at the left. a. Based on these data, estimate the height of a stack ofany50 pennies. How accurate is your estimate, at 95%confidence?

Answers: 1

Show answers

Answers

Answer from: nrosario33

The question is incomplete. Here is the complete question.

You are designing an automatic coin counter that stacks 50 pennies at a time to be placed in coin wrappers. You plan on measuring the height of the stack to determine the number of coins, but are concerned as to how accurate the method will be. You measure the thickness of 30 penniesm with the data listed below.

a. Based on these data, estimate the height of a stack of any 50 pennies. How accurate is your estimate, at 95% confidence?

b. What percentage of pennies from the population have thickness of at least 1.34mm?

a. Height = 74.25mm with margin of error of 0.021.

b. 99.38%

Step-by-step explanation:

a. To estimate the height of any 50 pennies, we have to determine the average of thickness of the sample given in the table.

Average is calculated as the sum of all the data divided by the quantity the sample has, so:

$\overline{x}=\frac{\Sigma x}{n}$

$\overline{x}=\frac{44.56}{30}$

$\overline{x}=1.485$

Each coin is estimated to have 1.485 mm of thickness. Then, the height of 50 pennies is

h = 1.485*50

h = 74.25

50 pennies will have an estimate height of 74.25 mm.

Margin of Error expresses the amount of random sampling error the results in a survey can have. It will show how many percentage points the result is from the actual population value.

To calculate it, we have to determine standard deviation of the data.

Standard deviation is

$s=\sqrt{\frac{\Sigma (x-\overline{x})^{2}}{n-1} }$

$s=\sqrt{\frac{0.09735}{29} }$

s = 0.058

For a 95% confidence, z-score is 1.96.

Margin is

$E=z.\frac{s}{\sqrt{n}}$

$E=1.96(\frac{0.058}{\sqrt{30}})$

E = 0.021

The accuracy of the estimate is 2.1%.

b. The percentage of pennies with thickness at least 1.34mm is represented as P(x>1.34). To calculate it:

P(x>1.34) = 1 - P(x<1.34)

Now, we have to normalize the data:

$z=\frac{x-\mu}{\sigma}$

$z=\frac{1.34-1.485}{0.058}$

z=-2.5

P(x

Consulting the z table,

P(z 0.00621

Now, for the percentage:

P(x1.34)=1-0.00621

P(x > 1.34) = 0.9938 or 99.38%

The percentage of pennies with thickness of at least 1.34mm is 99.38%.

You are designing an automatic coin counter that stacks 50 pennies at a time to be placed in coin wr

Answer from: Quest

answer: dead jah

step-by-step explanation:

bullet + jah= dead jah

Answer from: Quest

X=3 and y=4 is the answer

Another question on Mathematics

Mathematics, 21.06.2019 19:30

Acar started driving from city a to city b, distance between which is 620 miles, at a rate of 60 mph. two hours later a truck left city b and started moving towards city a at a rate of 40 mph. how many hours after the truck's departure will the two meet?

Answers: 1

Answer

Mathematics, 21.06.2019 20:40

If the endpoints of the diameter of a circle are (8, 6) and (2,0), what is the standard form equation of the circle? a) (x + 5)2 + (y + 3)2 = 18 (x + 5)2 + (y + 3)2 = 3.72 (x - 5)2 + (y - 3)2 = 18 d) (x - 5)2 + (y - 3)2 = 32

Answers: 1

Answer

Mathematics, 21.06.2019 22:30

The area of the map is the product of the length and width. write and expression for the area as the product of the two binomials do not multiply

Answers: 2

Answer

Mathematics, 22.06.2019 00:00

Mila's dog weighs 4 pounds more than 8 times the weight of keiko's dog. which expression could be used to fine te weight of mila's dog?

Answers: 2

Answer

You know the right answer?

You are designing an automatic coin counter that stacks 50 pennies at a time to be placed in coin wr...