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
Andreas93 [3]
3 years ago
12

A student takes an exam containing 1414 multiple choice questions. The probability of choosing a correct answer by knowledgeable

guessing is 0.30.3. At least 99 correct answers are required to pass. If the student makes knowledgeable guesses, what is the probability that he will pass? Round your answer to four decimal places.
Mathematics
1 answer:
Readme [11.4K]3 years ago
6 0

Answer:

0.0082 = 0.82% probability that he will pass

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the students guesses the correct answer, or he guesses the wrong answer. The probability of guessing the correct answer for a question is independent of 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.

In this problem we have that:

n = 14, p = 0.3.

If the student makes knowledgeable guesses, what is the probability that he will pass?

He needs to guess at least 9 answers correctly. So

P(X \geq 9) = P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14)

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

P(X = 9) = C_{14,9}.(0.3)^{9}.(0.7)^{5} = 0.0066

P(X = 10) = C_{14,10}.(0.3)^{10}.(0.7)^{4} = 0.0014

P(X = 11) = C_{14,11}.(0.3)^{11}.(0.7)^{3} = 0.0002

P(X = 12) = C_{14,12}.(0.3)^{12}.(0.7)^{2} = 0.000024

P(X = 13) = C_{14,13}.(0.3)^{13}.(0.7)^{1} = 0.000002

P(X = 14) = C_{14,14}.(0.3)^{14}.(0.7)^{0} \cong 0

P(X \geq 9) = P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) = 0.0066 + 0.0014 + 0.0002 + 0.000024 + 0.000002 = 0.0082

0.0082 = 0.82% probability that he will pass

You might be interested in
Find the equation of the line with slope 3/7 and that passes through the point (14, 0). Write your answer in the form y = mx + b
Allushta [10]

Answer:

y = 3/7x - 6

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Order of Operations: BPEMDAS
  • Equality Properties

<u>Algebra I</u>

Slope-Intercept Form: y = mx + b

  • m - slope
  • b - y-intercept

Step-by-step explanation:

<u>Step 1: Define</u>

Slope <em>m</em> = 3/7

Point (14, 0)

<u>Step 2: Find y-intercept </u><em><u>b</u></em>

  1. Substitute:                    0 = 3/7(14) + b
  2. Multiply:                        0 = 6 + b
  3. Isolate <em>b</em>:                       -6 = b
  4. Rewrite:                         b = -6

<u>Step 3: Write linear equation</u>

y = 3/7x - 6

7 0
3 years ago
If you share 7 apples equally with 3 people then there are 2 1/3. Frost complete the sentence. Then , briefly explain what the w
8090 [49]

Answer:

The whole number 2 is the number of whole apples each person gets.  The numerator 1 is the number of pieces of the remaining apple each person gets; the denominator 3 is the number of pieces the remaining apple is cut into.

8 0
2 years ago
The cost of safely disposing/A of the toxic chemicals is approximately/B
melomori [17]

The cost of safely disposing of the toxic chemicals is approximately five times what the company paid to purchase it.(Option D)

<h3>What is sentence correction?</h3>

Sentence correction or sentence improvement is a type of grammatical practice where a sentence is given with a word or a phrase that requires grammatical changes or improvement.

Now,

  • Here, we are talking about "toxic chemicals", that is "plural" but in the Part D of the sentence, "it" refers to the singular chemical.

Hence, the correction needs to be made at Option D; the correction would be: "paid to purchase them."

To learn more about sentence correction, refer to the link: brainly.com/question/14632568

#SPJ4

3 0
2 years ago
What is 7 x 10^22 in its expanded form?
sammy [17]

Answer:

70,000,000,000,000,000,000,000

Step-by-step explanation:

3 0
3 years ago
Consider that the roots of a cubic equation with integral coefficients are 1, −2, and 3.
Iteru [2.4K]

Answer:

The answer is option A) X + 2

Step-by-step explanation:

Any polynomial of order n can be expressed in terms of their roots in factors of the form

(x-a)(x-b)(x-c)(x-d)....... = 0

Where a,b,c,d,... are the roots of the polynomial

In the example shown

(x+2) = (x-(-2))

And -2 happens to be the root of the polynomial in question

3 0
3 years ago
Read 2 more answers
Other questions:
  • Cary's barbecue sauce recipe calls for 2 2/3 cups of water for every 8 pints of tomato sauce. How many cups of water does cary u
    11·2 answers
  • What is the solution to –4(8 – 3x) ≥ 6x – 8?<br><br> x ≥ –4/3<br> x ≤ –4/3<br> x ≥ 4<br> x ≤ 4
    14·1 answer
  • A helicopter hovers 500 feet above a small island. The figure shows that the angle of depression from the helicopter to point p
    12·1 answer
  • Help meeeeeeeeeeeeeee
    10·2 answers
  • Write the example about adding and subtracting decimals
    11·1 answer
  • Help pls
    10·1 answer
  • Need help asap please!!
    11·1 answer
  • A boat travels 475 miles in 30
    13·1 answer
  • Please answer the question correctly with factual information for brainliest.
    8·1 answer
  • What is the midpoint formula
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!