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
Romashka [77]
3 years ago
10

A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 stude

nts registered for the course. Compute the probability that 2 or fewer will withdraw (to 4 decimals). Compute the probability that exactly 4 will withdraw (to 4 decimals). Compute the probability that more than 3 will withdraw (to 4 decimals). Compute the expected number of withdrawals.
Mathematics
1 answer:
EleoNora [17]3 years ago
3 0

Answer:

a) P(X \leq 2)= P(X=0)+P(X=1)+P(X=2)

And we can use the probability mass function and we got:

P(X=0)=(20C0)(0.2)^0 (1-0.2)^{20-0}=0.0115  

P(X=1)=(20C1)(0.2)^1 (1-0.2)^{20-1}=0.0576  

P(X=2)=(20C2)(0.2)^2 (1-0.2)^{20-2}=0.1369  

And adding we got:

P(X \leq 2)=0.0115+0.0576+0.1369 = 0.2061

b) P(X=4)=(20C4)(0.2)^4 (1-0.2)^{20-4}=0.2182  

c) P(X>3) = 1-P(X \leq 3) = 1- [P(X=0)+P(X=1)+P(X=2)+P(X=3)]

P(X=0)=(20C0)(0.2)^0 (1-0.2)^{20-0}=0.0115  

P(X=1)=(20C1)(0.2)^1 (1-0.2)^{20-1}=0.0576  

P(X=2)=(20C2)(0.2)^2 (1-0.2)^{20-2}=0.1369

P(X=3)=(20C3)(0.2)^3 (1-0.2)^{20-3}=0.2054

And replacing we got:

P(X>3) = 1-[0.0115+0.0576+0.1369+0.2054]= 1-0.4114= 0.5886

d) E(X) = 20*0.2= 4

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  

Let X the random variable of interest, on this case we now that:  

X \sim Binom(n=20, p=0.2)  

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 a

We want this probability:

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

And we can use the probability mass function and we got:

P(X=0)=(20C0)(0.2)^0 (1-0.2)^{20-0}=0.0115  

P(X=1)=(20C1)(0.2)^1 (1-0.2)^{20-1}=0.0576  

P(X=2)=(20C2)(0.2)^2 (1-0.2)^{20-2}=0.1369  

And adding we got:

P(X \leq 2)=0.0115+0.0576+0.1369 = 0.2061

Part b

We want this probability:

P(X=4)

And using the probability mass function we got:

P(X=4)=(20C4)(0.2)^4 (1-0.2)^{20-4}=0.2182  

Part c

We want this probability:

P(X>3)

We can use the complement rule and we got:

P(X>3) = 1-P(X \leq 3) = 1- [P(X=0)+P(X=1)+P(X=2)+P(X=3)]

P(X=0)=(20C0)(0.2)^0 (1-0.2)^{20-0}=0.0115  

P(X=1)=(20C1)(0.2)^1 (1-0.2)^{20-1}=0.0576  

P(X=2)=(20C2)(0.2)^2 (1-0.2)^{20-2}=0.1369

P(X=3)=(20C3)(0.2)^3 (1-0.2)^{20-3}=0.2054

And replacing we got:

P(X>3) = 1-[0.0115+0.0576+0.1369+0.2054]= 1-0.4114= 0.5886

Part d

The expected value is given by:

E(X) = np

And replacing we got:

E(X) = 20*0.2= 4

You might be interested in
What is the expression in simplest radical form?<br><img src="https://tex.z-dn.net/?f=%285x%5E%7B4%7D%20y%5E%7B3%7D%29%5E%7B%5Cf
Vlad [161]

Use the formula a^(x/n) = (n)√a^x   (note it is a small n)

(5x^4y^3)^(2/9) = Small 9

Convert.

\sqrt{9{{(25x^{8})y^9 }}} is your answer

hope this helps

5 0
3 years ago
Read 2 more answers
Please help and show work!!
Paladinen [302]

B. Because 20 is greter than 18.

6 0
3 years ago
Read 2 more answers
Is the discriminant of f positive , zero , or negative ​
Kruka [31]

Answer:

Negative because there's no x-intercepts!

Hope this helps!

8 0
3 years ago
A function g(x) has the points (-2, 8) and (2, 8 ) on its graph. Is the function:
Marianna [84]
The function is odd.
3 0
3 years ago
-3=x/-9 please tell me how to solve this I’m way behind and trying to learn thank you :)
snow_tiger [21]

-3 = x/-9

To make this easier, I'll put it in normal numbers

(-3 = x/-9) -1

3 = x/9

Multiply both sides by nine to take out the division.

27 = x

Hope that this helped!

8 0
3 years ago
Other questions:
  • Answer question from picture.
    11·1 answer
  • Please include how you got your answer.
    9·1 answer
  • 1.
    7·1 answer
  • A grading machine can grade 96 multiple
    13·1 answer
  • Emily is 4 years older than Grace. When their ages are added together they equal 26. How old is Emily?
    8·1 answer
  • Hurry! I need Help<br> Graph Y=5/3x-9<br> Where do i graph my points?
    13·2 answers
  • Which product is greater than 3/4?
    10·1 answer
  • can ace and expert help me in which number does 7 resent 10 times the value that it respesnts in 167 300​
    5·2 answers
  • Y=7/x, x≠0 need the graph answer!!
    11·1 answer
  • Can anyone help me with this?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!