1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Lena [83]
3 years ago
13

Suppose certain coins have weights that are normally distributed with a mean of 5.805 g5.805 g and a standard deviation of 0.071

g0.071 g. A vending machine is configured to accept those coins with weights between 5.6755.675 g and 5.9355.935 g. a. If 260260 different coins are inserted into the vending​ machine, what is the expected number of rejected​ coins?
Physics
1 answer:
stiks02 [169]3 years ago
8 0

Answer:

a) P(5.675

And the expected number would be 260*0.933=242.58 and n =243 rounded up.

b)P(5.675< \bar X

Explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

2) Part a

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

X \sim N(5.805,0.71)  

Where \mu=5.805 and \sigma=0.071

We are interested on this probability

P(5.675

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

If we apply this formula to our probability we got this:

P(5.675

And we can find this probability on this way:

P(-1.83

And the expected number would be 260*0.933=242.58 and n =243 rounded up.

3) Part b

If 260 different coins are inserted in the vending machine, what is the probability that the mean falls between the limits of 5.675 g and 5.935.

From the central limit theorem we know that the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

P(5.675< \bar X

You might be interested in
Which has the most kinetic energy?
lara31 [8.8K]

Answer:

I think A golf ball shot out of a small cannon

Explanation:

3 0
2 years ago
Which of the following is a non renewable resource?
Karo-lina-s [1.5K]
Carbon isn’t because all the others on the list are naturally made apart from carbon which is man made because of all the pollution . X
3 0
3 years ago
What is the name and symbol of the element in the second row and fourteenth column of the periodic table? Hint: Review your peri
Papessa [141]
The answer is Carbon. Beyond being the only element listed here that is located in the second row, it is also in the fourteenth column of the table if you count from left to right. Hope this helps!
4 0
3 years ago
Which is a consequence of the third law of thermodynamics Energy is not always conserved. Engines cannot discharge waste heat. H
miss Akunina [59]
Heat engines are less than 100% efficient because absolute zero cannot be reached
8 0
3 years ago
Read 2 more answers
Doc Brown has calculated his Delorean can accelerate at a rate of 2.52 m/s/s. How
GREYUIT [131]

Answer:

304.89m

Explanation:

Given

acceleration a = 2.52m/s²

final speed v = 39.2m/s

initial speed = 0m/s (car accelerates from rest)

Using the equation of motion below to get the distance of Doc brown from Marty;

v² = u²+2as

substitute the given parameters

39.2² = 0²+2(2.52)s

1536.64 = 0+5.04s

divide both sides by 5.04

1536.64/5.04 = 5.04s/5.04

rearrange the equation

5.04s/5.04 = 1536.64/5.04

s = 304.89m

Hence He and Marty must stand at 304.89m to allow the car to accelerate from rest to a speed  of 39.2 m/s?

6 0
3 years ago
Other questions:
  • What is the difference in the charges on a ballon rubbed in your hair and a glass rod rubbed
    5·1 answer
  • 1. I drop a penny from the top of the tower at the front of Fort Collins High School and it takes 1.85 seconds to hit the ground
    6·2 answers
  • Define light year please
    6·1 answer
  • Amit has found a rock in his backyard and would like to measure its mass, volume, and density. What tools can he use to perform
    10·1 answer
  • What is a measure of the pulling force of gravity?
    15·1 answer
  • After 2.0 s has elapsed on kara's watch, what does kara say the distance is between you and the laser pulse?
    14·1 answer
  • What type of relationship does this graph show?
    15·1 answer
  • An object is 70 um long and 47.66um wide. how long and wide is the object in km?​
    5·1 answer
  • 13. What is the acceleration of a 1,000-kilogram truck with a net force of 7,000 newtons?
    14·1 answer
  • How to find velocity of center of mass before and after the collision
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!