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
Masja [62]
3 years ago
6

For each random variable, state whether the random variable should be modeled with a Binomial distribution or a Poisson distribu

tion. Explain your reasoning. State the parameter values that describe the distribution and give the probability mass function.
Random Variable 1. A quality measurement for cabinet manufacturers is whether a drawer slides open and shut easily. Historically, 2% of drawers fail the easy slide test. A manufacturer samples 10 drawers from a batch. Assuming the chance of failure is independent between drawers, what type of distribution could be used to model the number of failed drawers from the sample of 10?

Random Variable 2. The warranty for a particular system on a new car is 2 years. During which there is no limit to the number of warranty claims per car. Historically, the average number of claims per car during the period is 0.8 claims. What type of distribution could be used to model the number of warranty claims per car?
Mathematics
1 answer:
navik [9.2K]3 years ago
7 0

Answer:

1) This random variable should be modelled using a binomial distribution since we have independence between the events and a bernoulli trial each time when the experiment is conducted, a fixd value for the sample size n and for the probability of success.

Let X the random variable of interest, on this case th distribution would be given by:

X \sim Binom(n=10, p=0.02)

The probability mass function for the Binomial distribution is given as:

P(X)=(nCx)(p)^x (1-p)^{n-x} = (10Cx) (0.02)^x (1-0.02)^{10-x}

2) For this case we don't have a sample size provided and we just have an average rate for a given period, so then we can assume that the best distribution for this case is the Poisson distribution.

Let X the random variable that represent the number of claims per car. We know that X \sim Poisson(\lambda)

The probability mass function for the random variable is given by:

f(x)=\frac{e^{-\lambda} \lambda^x}{x!} , x=0,1,2,3,4,...

Where \lambda=0.2 represent the mean of occurrences in the interval of 2 years provided.

And f(x)=0 for other case.

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Random variable 1

This random variable should be modelled using a binomial distribution since we have independence between the events and a bernoulli trial each time when the experiment is conducted, a fixd value for the sample size n and for the probability of success.

Let X the random variable "number of failed drawers", on this case th distribution would be given by:

X \sim Binom(n=10, p=0.02)

The probability mass function for the Binomial distribution is given as:

P(X)=(nCx)(p)^x (1-p)^{n-x} = (10Cx) (0.02)^x (1-0.02)^{10-x}

Where (nCx) means combinatory and it's given by this formula:

nCx=\frac{n!}{(n-x)! x!}

Random variable 2

For this case we don't have a sample size provided and we just have an average rate for a given period, so then we can assume that the best distribution for this case is the Poisson distribution.

Let X the random variable that represent the number of claims per car. We know that X \sim Poisson(\lambda)

The probability mass function for the random variable is given by:

f(x)=\frac{e^{-\lambda} \lambda^x}{x!} , x=0,1,2,3,4,...

Where \lambda=0.2 represent the mean of occurrences in the interval of 2 years provided.

And f(x)=0 for other case.

You might be interested in
Internal control over a​ company's assets should include the following​ policy:
Molodets [167]

The answer is C because I can c the answer right in front of me

8 0
3 years ago
Help please i need this done!!
Juliette [100K]

Answer:

True, True, True, False

Step-by-step explanation:

8 0
2 years ago
ANSWER QUICK AND I WILL MAKE YOU BRAINLIEST
alekssr [168]

Answer:

The width of the window should be 7.6\ ft and the height of the window should be 3.8\ ft

Step-by-step explanation:

we know that

The circumference of a semicircle (window) is equal to

C=\pi r

we have that

C=12\ ft

\pi=3.14

substitute and solve for r

12=(3.14)r

r=12/3.14=3.8\ ft

so

the width of the window is equal to the diameter of the semicircle

so

The width of the window should be 3.8*2=7.6\ ft and the height of the window should be 3.8\ ft

4 0
3 years ago
Find the length of the picture frame whose width is 3 inches and whose proportions are the same as 9- inches by 12-inch long fra
andrew11 [14]

Answer:

9-

Step-by-step explanation: 9-

4 0
3 years ago
The heat developed in an electric wire varies jointly as the wires resistance, the time the current flows, & the square of t
never [62]

Answer:

4 ohms

Step-by-step explanation:

The question is "In two minutes a current of 5 amps develops 1,200 heat units in a wire of 8 ohms resistance. What resistance does a similar wire have, which develops 6,000 heat units with a current of 10 amps in 5 minutes?"

Current, I₁ = 5 A

Heat, Q₁ = 1200 units

Resistance, R₁ = 8 ohms

Time, t₁ = 2 min = 120 s

New heat, Q₂ = 6000 units

Current, I₂ = 10 A

New time, t₂ = 5 min = 300 s

We need to find the new resistance.

Heat developed is given by :

Q=I^2Rt

\dfrac{Q_1}{I_1^2R_1t_1}=\dfrac{Q_2}{I_2^2R_2t_2}\\\\R_2=\dfrac{Q_2\times I_1^2R_1t_1}{Q_1I_2^2t_2}\\\\R_2=\dfrac{6000\times 5^2\times 8\times 120}{1200\times 10^2\times 300}\\\\=4\ \Omega

So, the new resistance is 4 ohms.

5 0
3 years ago
Other questions:
  • Craig has the following set of 13 cards. If a card is randomly chosen from Craig’s set, what is the probability that the card wi
    5·1 answer
  • Jalen plots two integers on a horizontal number line. The leftmost integer is negative. Which must be true of the second integer
    8·2 answers
  • Graph the equation y=x²-8x+7 on the accompanying set of axes. You must plot 5 points including the roots and the vertex.
    8·1 answer
  • What is the answer to (3x-15) degrees
    14·1 answer
  • How can you describe the relationships among angles and sides in a triangle?
    8·1 answer
  • A car drives 215 km east and then 45 km north. What is the magnitude of the car’s displacement? Round your answer to the nearest
    10·2 answers
  • Jack needs 22 pirates for every 2 pirate ships he manages
    15·1 answer
  • Which of the sets of ordered pairs represents a function? (1 point) A = {(2, 7), (1, −5), (7, 2), (2, −9)} B = {(5, 3), (−2, −9)
    13·1 answer
  • Choose the best graph for the equation y=3x+2
    5·2 answers
  • Graph the following log function and describe the key characteristics (Domain, range, asymptote, shifts, intercepts): f(x) = log
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!