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
DiKsa [7]
3 years ago
8

Each multiple-choice question on an exam has four choices. Suppose that there are 10 questions and the choice is selected random

ly and independently for each question. Let X denote the number of questions answered correctly. Does X have a discrete uniform distribution? Why or why not?
Mathematics
1 answer:
Anika [276]3 years ago
3 0

Answer:

It is discrete, but not uniform, since each outcome is not equally as likely.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either it is answered correctly, or it is not. The probability of answered a question is independent from the probability of answeing other questions. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

Each multiple-choice question on an exam has four choices.

This means that p = \frac{1}{4} = 0.25

10 questions

This means that n = 10

Let X denote the number of questions answered correctly. Does X have a discrete uniform distribution? Why or why not?

It is discrete, because the number of questions answered correctly is a discrete value.

However, it is not uniform. A distribution is uniform when each outcome is equally as likely. For example, the probability of answering 0 questions correctly is different of the probability of answering 1 question correctly, as we see below.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{10,0}.(0.25)^{0}.(0.75)^{10} = 0.0563

P(X = 1) = C_{10,1}.(0.25)^{1}.(0.75)^{9} = 0.1877

You might be interested in
I need help please?!!!!
Oksanka [162]

Answer:

69 420

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and sodium chlorate to evaporate
Setler79 [48]

Answer:

48 mm ^ 2

Step-by-step explanation:

We know we have a cube of side x, therefore the volume of that cube will be equal to:

V = x ^ 3, because it is a cube and each side is the same.

Now the derivative of the volume with respect to the length (that is, x) would be:

dV / dx = 3 * (x ^ 2)

They tell us that x takes a value of 4, replacing we have:

dV / dx = 3 * (4 ^ 2) = 48

That is, 48 mm ^ 2 would be the value of dV / dx when x is equal to 4 mm.

6 0
3 years ago
Which of the following ratios is equivalent to the ratio 3:4?
natta225 [31]
What’re the choices you have
6 0
2 years ago
Read 2 more answers
What is the solution for x in the equation?<br><br> 10x − 4.5 + 3x = 12x − 1.1
Aleksandr [31]

Answer:in first part of equation add 10x and 3x (like terms)

13x-4.5=12x-1.1

move all terms containing x to left side of equation

13x-4.5-12x= -1.1

x-4.5= -1.1

Subtract 4.5 from both sides

x=3.4

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Pls ans both the questions im very confused
lions [1.4K]

Answer:

Step-by-step explanation:

In Δ PQS and ΔPQT

∠QPS = ∠RPT       {Common angle}

∠PSQ = ∠PTR = 90°         {QS & RT are altitude}

QS = RT                            {given}

ΔPQS ≅ ΔPRT               {A A S congruent}

PQ = PS                         {CPCT}

So, PQR is an isosceles triangle.

9)

a) Flas card (I) and (iii) are congruent.

b)  A S A congruent

c) BC ≅ RP

5 0
2 years ago
Other questions:
  • What is the value of X? Make sure to show all of your work!
    8·1 answer
  • Three to the sixth power divided by three to the third power
    5·1 answer
  • Which system represents the graph?
    11·2 answers
  • Look at a picture of the American flag. Approximately what<br> part of the flag is blue? Explain.
    11·2 answers
  • Please help, thanks if you do
    12·2 answers
  • - Which values are equivalent to b in the equation below? 62 = 12 Select all that apply. A. -6 B. 6 C.-V12 D. 112 E. -144 F. 144
    5·1 answer
  • The population standard deviation for the heights of dogs, in inches, in a city is 3.4 inches. If we want to be 90% confident th
    10·1 answer
  • . A un concierto asistieron 10000 personas , lo que representó un total de
    5·1 answer
  • If x is domain and y is range, why am I Mexican?
    7·1 answer
  • What is 5 divided by 9?
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!