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
weeeeeb [17]
3 years ago
8

A school newspaper reporter decides to randomly survey 12 students to see if they will attend Tet (Vietnamese New Year) festivit

ies this year. Based on past years, she knows that 18% of students attend Tet festivities. We are interested in the number of students who will attend the festivities.
a. In words, define the random variable X.

b. List the values that X may take on.

c. Give the distribution of X.

d. How many of the 12 students do we expert to attend the festivities?

e. Find the probability that at most four students will attend.

f. Find the probability that more than two students will attend.
Mathematics
1 answer:
marta [7]3 years ago
7 0

Answer:

a) Let X the random variable of interest "number of students who attend the Tet festivities",

b) The possible values for the random variable X are : 0,1,2,3,4,5,6,7,8,9,10,11,12

c) The distribution for X on this case is given by:

X \sim Binom(n=12, p=0.18)

d) E(X) = np = 12*0.18=2.16

e) P(X \leq 4)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)=0.9511

f) P(X>2) =1-P(X\leq 2) =1-[P(X=0)+P(X=1)+P(x=2)]=1-[0.09242+0.24345+0.29392]=0.3702

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".

Solution to the problem

Part a

Let X the random variable of interest "number of students who attend the Tet festivities",

Part b

The possible values for the random variable X are : 0,1,2,3,4,5,6,7,8,9,10,11,12

Part c

The distribution for X on this case is given by:

X \sim Binom(n=12, p=0.18)

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

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

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

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

Part d

The expected value for the binomial distribution is given by:

E(X) = np = 12*0.18=2.16

Part e

For this case we want this probability:

P(X \leq 4)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)

P(X=0)=(12C0)(0.18)^0 (1-0.18)^{12-0}=0.09242

P(X=1)=(12C1)(0.18)^1 (1-0.18)^{12-1}=0.24345

P(X=2)=(12C2)(0.18)^2 (1-0.18)^{12-2}=0.29392

P(X=3)=(12C3)(0.18)^3 (1-0.18)^{12-3}=0.21506

P(X=4)=(12C4)(0.18)^4 (1-0.18)^{12-4}=0.10622

P(X \leq 4)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)=0.9511

Part f

For this case we want this probability:

P(X>2)

And we can use the complement rule to find this like that:

P(X>2) =1-P(X\leq 2) =1-[P(X=0)+P(X=1)+P(x=2)]

P(X>2) =1-P(X\leq 2) =1-[P(X=0)+P(X=1)+P(x=2)]=1-[0.09242+0.24345+0.29392]=0.3702

You might be interested in
The cost of five books is 71 dollars what is the cost of each book
Sedbober [7]
Divide 71 and 5 to get a decimal since 71 does not end with 5 or 0. Do it to get 14 1/5 or 14.2
5 0
3 years ago
Read 2 more answers
Solve for x please thanks​
N76 [4]

Answer:

32

Step-by-step explanation:

So, lets go over what we know:

The equation to find x is the same on both sides.

Now, lets find this equation:

So, the total area of the two lines on the left side of the triangle are 24.

Lets first subtract the first line from the total of the two lines to find the value of the second line:

24-3

=

21.

Now that we know the value of the 2nd line is 21. lets divide it by the first line(3) to find the scale factor:

21/3

=

7

So the scale factor is 7!

Lets plug this in for x.

We know that the first line is 4.

The second line is 7x bigger than 4.

So we can calculate this as:

7x4

=

28

So x is 28!

This is your answer!

Hope it helps! :)

6 0
3 years ago
Is the quotient positive or negitive
ArbitrLikvidat [17]
I guess positive bcuz - -=+
6 0
3 years ago
Read 2 more answers
A square has vertices at the points A(-4,-4), B(-5,-4), C(-5,-3), and D(-4,-3). What is the area of this square? A. 1 square uni
laiz [17]

Answer:

Step-by-step explanation:

The length of AB = 1 unit.

area of square = 1² unit² = 1 square unit.

8 0
3 years ago
What are the next letters BE GL LO QT
Tpy6a [65]
What are we supposed to be basing this off of? is there no additional information?
8 0
3 years ago
Other questions:
  • Choose all items which are true.
    8·1 answer
  • solve this problem so the hiking trails in roman nose park are 3.6, 7.9, 10.4, 5.7, and 3.5 miles long. Cindy and Geoff hiked tw
    13·1 answer
  • Please help me!! 10 points!!
    6·1 answer
  • How do i figure this out and get the correct answer?
    14·1 answer
  • The equation of a circle centered at the origin is x2 + y2 = 16. What is the radius of the circle?
    5·2 answers
  • Round 1001 to the nearest thousand.
    14·1 answer
  • If y varies directly as x, and y=-4 when x=8, find y when x=3
    13·1 answer
  • 59:
    10·1 answer
  • How much would a $1.99 box of ziploc bags cost after 6% sales tax
    13·1 answer
  • Help please <br><br><br><br><br><br><br><br><br><br><br> !!!!!!!!!!!!!!!!!!
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!