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
Alexxx [7]
4 years ago
13

A statistics professor finds that when he schedules an office hour for student help, an average of 3.3 students arrive. Find the

probability that in a randomly selected office hour, the number of student arrivals is 6.
Mathematics
2 answers:
butalik [34]4 years ago
7 0

Answer:

P(X=6)

If we use the probability mass function we got:

P(X=6) = \frac{e^{-3.3} 3.3^6}{6!}= 0.0662

Step-by-step explanation:

Previous concepts

The Poisson process is useful when we want to analyze the probability of ocurrence of an event in a time specified. The probability distribution for a random variable X following the Poisson distribution is given by:

Solution to the problem

Let X the random variable that represent the number of students arrive at the office hour. We know that X \sim Poisson(\lambda=3.3)

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,...

And f(x)=0 for other case.

For this distribution the expected value is the same parameter \lambda

E(X)=\mu =\lambda=3.3

And we want this probability:

P(X=6)

If we use the probability mass function we got:

P(X=6) = \frac{e^{-3.3} 3.3^6}{6!}= 0.0662

Vlad [161]4 years ago
5 0

Answer:

0.0662

Step-by-step explanation:

The given problem indicates the Poisson experiment.

The pdf of Poisson experiment is as follow

P(X=x)=μ^x(e^-μ)/x!

Here, the average student visits in office hour=3.3=μ.

We have to find the probability that the number of student arrivals is 6 in a randomly selected office hour.

So, x=6 and μ=3.3

The probability that the number of student arrivals is 6 in a randomly selected office hour

P(X=6)=3.3^6(e^-3.3)/6!

P(X=6)=1291.468(.0369)/720

P(X=6)=47.6552/720

P(X=6)=0.0662.

Thus, the probability that the number of student arrivals is 6 in a randomly selected office hour is 6.62 or 0.0662.

You might be interested in
A.
Digiron [165]
Given:

<span>The average number of daylight hours each month in Springfield in 2015:

Jan   9.5
Feb  10.5
Mar  12
Apr  13.25
May  14.5
Jun   15
Jul    14.75
Aug   13.75
Sep    12.5
Oct    11.0
Nov   9.75
Dec   9.25

Now, we observe the trend of the monthly hours, it starts with a low value then increases and decreases back to the original value. This represents a parabola with the highest point of 15 hours. </span><span />
5 0
3 years ago
Sierra's ice cream shop made $45 before she had to close early when the power went out. She realized she lost Two-thirds of a do
Troyanec [42]

Answer:

the profit in the case when the shop is closed for 6 hours is $41

Step-by-step explanation:

The computation of the profit in the case when the shop is closed for 6 hours is shown below:

= Expression of the situation × number of hours in which the shop is closed

= 45 - 2 ÷ 3 × 6 hours

= $41

hence, the profit in the case when the shop is closed for 6 hours is $41

Therefore the third option is correct

6 0
3 years ago
Read 2 more answers
A 2-yard piece of copper wire costs $68.70. What is the price per foot?
klio [65]

Answer:

hey hey hey hey hye hye  heyr32klq,adm.

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Which statement is true?
erastovalidia [21]

Answer:

A square is always a rhombus.

Explanation:

A square has 4 sides of equal length.

5 0
3 years ago
Read 2 more answers
H(x) = √x-10 Determine for each x-value whether it is in the domain of h or not.
Lesechka [4]

Answer:

0 is not in domain

5 is not in domain

10 is in domain

Step-by-step explanation:

10 is in domain because inputting 10 into the function gives an output of 0

0 is not in th domain because 0 gives us the square root of a negative number, and the quare of a negative number isnt a real number

5 is not in the domain for the same reason

5 0
3 years ago
Other questions:
  • What is the height of a cylinder?
    13·1 answer
  • HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!
    10·1 answer
  • One number is three times another number. If the sum of the numbers is 36, determine the two
    13·1 answer
  • What is the value of x in the equation 2/3
    11·1 answer
  • Bag with 4 red tiles, 5 blue tiles,6 green tiles, and 2 yellow tiles. What is the probability of yellow or blue?
    8·2 answers
  • Marcus wrote an expression equivalent to 7(x+8). Liz wrote a different expression that has the same value as Marcus’ expression
    7·1 answer
  • Please help me out!​
    7·1 answer
  • Help- No silly answers
    10·1 answer
  • A window is in the shape of a kite. caleb wants to apply a layer of plastic film on the top half of the window so that the glass
    13·1 answer
  • What shape always has four congruent sides
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!