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
zzz [600]
3 years ago
14

Orders arrive at a Web site according to a Poisson process with a mean of 11 per hour. Determine the following: a) Probability o

f no orders in five minutes. Round your answer to three decimal places (e.g. 98.765). Enter your answer in accordance to the item a) of the question statement b) Probability of 3 or more orders in five minutes. Round your answer to three decimal places (e.g. 98.765). Enter your answer in accordance to the item b) of the question statement c) Length of a time interval such that the probability of no orders in an interval of this length is 0.001. Round your answer to two decimal places (e.g. 98.76).
Mathematics
1 answer:
Nataliya [291]3 years ago
7 0

Answer:

a) 0.39984 = 39.984% probability of no orders in five minutes.

b) 0.06563 = 6.563% probability of 3 or more orders in five minutes.

c) The length of time is 0.63 hours

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\mu is the mean in the given interval.

Orders arrive at a Web site according to a Poisson process with a mean of 11 per hour.

This means that \mu = 11h, in which h is the number of hours.

a) Probability of no orders in five minutes.

Five minutes means that h = \frac{5}{60} = \frac{1}{12}, so \mu = \frac{11}{12} = 0.9167

This probability is P(X = 0). So

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

P(X = 0) = \frac{e^{-0.9167}*(0.9167)^{0}}{(0)!} = 0.39984

0.39984 = 39.984% probability of no orders in five minutes.

b) Probability of 3 or more orders in five minutes.

This is:

P(X \geq 3) = 1 - P(X < 3)

In which

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

So

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

P(X = 0) = \frac{e^{-0.9167}*(0.9167)^{0}}{(0)!} = 0.39984

P(X = 1) = \frac{e^{-0.9167}*(0.9167)^{1}}{(1)!} = 0.36653

P(X = 2) = \frac{e^{-0.9167}*(0.9167)^{2}}{(2)!} = 0.168

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.39984 + 0.36653 + 0.168 = 0.93437

P(X \geq 3) = 1 - P(X < 3) = 1 - 0.93437 = 0.06563

0.06563 = 6.563% probability of 3 or more orders in five minutes.

c) Length of a time interval such that the probability of no orders in an interval of this length is 0.001.

This is h for which:

P(X = 0) = 0.001

We have that:

P(X = 0) = e^{-\mu}

And

\mu = 11h

So

P(X = 0) = 0.001

e^{-11h} = 0.001

\ln{e^{-11h}} = \ln{0.001}

-11h = \ln{0.001}

h =-\frac{\ln{0.001}}{11}

h = 0.63

The length of time is 0.63 hours

You might be interested in
What is the difference <br> A <br> B<br> C<br> D
aksik [14]

Answer:

D. \frac{x-1}{x^2+3x+2}}

Step-by-step explanation:

The given expression is;

\frac{x}{x^2+3x+2}-\frac{1}{(x+2)(x+1)}

This is the same as;

\frac{x}{(x+2)(x+1)}-\frac{1}{(x+2)(x+1)}

The denominators are the same.

Subtract the numerators and write one denominator;

\frac{x-1}{(x+2)(x+1)}}

Rewrite to get;

\frac{x-1}{x^2+3x+2}}

4 0
3 years ago
Jordan and Ellen recycle cans. Jordan recycles 7 cans for every 12 cans Ellen recycles. Last week, Jordan
Natasha2012 [34]

Answer:

c=6 They sold a total of 114 cans

Step-by-step explanation: The ratio is 7:12, so last week, he sold 42 cans, meaning that you need to divide 42 by to get 6 in order to figure out the amount Ellen sold last week. Then do 6 times 12 to get 72 cans sold for Ellen. Add 72 to 42 to get 114 cans sold in total.

5 0
3 years ago
Read 2 more answers
What dvision problem can be represented using the number line?
Anon25 [30]

Answer:

C

Step-by-step explanation:

6 0
2 years ago
Amy ate 7 candies out of a chocolate box. In other words she ate 28%of the candies. What is the total number of candies in the b
kari74 [83]
Answer : 35



You have to do 28 plus 7






And u would get ur answer
6 0
3 years ago
Read 2 more answers
Given the equation for the total surface area of a cylinder, solve for the height of the cylinder.
schepotkina [342]
H= (2pier^2)/ 2pier all subtracted by s so the last equation from the picture.
Hope it helps!
4 0
3 years ago
Read 2 more answers
Other questions:
  • A hemisphere with a 90 degree slice removed and a radius of 8 what is the volume
    10·1 answer
  • Need help finding angles JK
    9·2 answers
  • What is the area in square units of the triangle formed by points (-3,1) (-3,5) and (4,1)
    5·1 answer
  • SOMEBODY HELP!
    11·1 answer
  • If a hurricane was headed your way, would you evacuate? The headline of a press release issued January 21, 2009 by the survey re
    10·1 answer
  • Find the retail price if original cost is $45 and markup 20%
    5·2 answers
  • You put 500 dollars into your savings account. Your bank account offers a yearly interest rate of 3.5% and you leave the money i
    5·1 answer
  • I have to pass pls help
    12·1 answer
  • ASAP pls it’s due tomorrow
    6·2 answers
  • Figure this out for me!! (60 pts)
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!