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
worty [1.4K]
3 years ago
13

You are to take a multiple-choice exam consisting of 64 questions with 5 possible responses to each question. Suppose that you h

ave not studied and so must guess (select one of the five answers in a completely random fashion) on each question. Let x represent the number of correct responses on the test. (a) What is your expected score on the exam? (Hint: Your expected score is the mean value of the x distribution.)(b) Compute the variance and standard deviation of x. Variance =Standard deviation
Mathematics
1 answer:
damaskus [11]3 years ago
5 0

Answer:

a) Expected score on the exam is 12.8.

b) Variance 10.24, Standard deviation 3.2

Step-by-step explanation:

For each question, there are only two possible outcomes. Either you guesses the answer correctly, or you does not. The probability of guessing the answer of a question correctly is independent of other questions. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

E(X) = np

The variance of the binomial distribution is:

V(X) = np(1-p)

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

64 questions.

So n = 64

5 possible answers, one correctly, chosen at random:

So p = \frac{1}{5} = 0.2

(a) What is your expected score on the exam?

E(X) = np = 64*0.2 = 12.8

(b) Compute the variance and standard deviation of x. Variance =Standard deviation

V(X) = np(1-p) = 64*0.2*0.8 = 10.24

Variance 10.24

\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{64*0.2*0.8} = 3.2

Standard deviation 3.2

You might be interested in
Identify the property. ( x + y ) + z = x + ( y + z )
klemol [59]

Answer: Associative Property

Step-by-step explanation:

4 0
3 years ago
Please help me guys please
hram777 [196]

c. the number of persons allegric to penicillin

6 0
2 years ago
Can someone pls help with this
Anon25 [30]

Answer:

sorry i cant figure this out

7 0
3 years ago
Dale drove 441 miles in 7 hours. At the same rate, how long would it take him to drive 315 miles?​
AURORKA [14]

Answer:

5 Hours

Step-by-step explanation:

He’s going 63 MPH

441/7 = 63 MPH

315/63 = 5 Hours

5 0
2 years ago
Read 2 more answers
One number is 9 more than twice another. If their difference is 22, what is the larger number? 133135
adoni [48]

ANSWER :

The larger number is 35

EXPLANATION :

Let x = first number

The second number is 9 more than twice the other number.

So that will be (2x + 9)

The difference between the two is 22.

So we have :

\begin{gathered} (2x+9)-x=22 \\ x+9=22 \\ x=22-9 \\ x=13 \end{gathered}

The first number is 13

The second number will be :

2(13) + 9 = 26 + 9

= 35

7 0
1 year ago
Other questions:
  • What is the patterns of 1,4,9,16​
    15·2 answers
  • What is the area of the rectangle? DO NOT ROUND.
    14·1 answer
  • How do I solve 3xy-2x= 17
    10·1 answer
  • Transform the given quadratic function into vertex form f(x) = quadratic function into vertex form f(x) = quadratic function int
    9·1 answer
  • A rhombus diagonals bisects opposite <br>a)angles <br>b)line​
    11·2 answers
  • What is the equation of the line that passes through the point (-4,7) and has an undefined slope?
    8·1 answer
  • Find the 12th term of the geometric sequence 5, 20, 80, ...
    8·1 answer
  • HELP PLEASE!! WHAT IS 9+3 8/2
    6·2 answers
  • From a hot-air balloon, Guadalupe measures a 31^{\circ} ∘ angle of depression to a landmark that’s 316 feet away, measuring hori
    5·1 answer
  • The volume of a cube is 64 cubic feet. What are the lengths of the side of the cube?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!