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klio [65]
3 years ago
14

On a multiple choice test with 15 ​questions, each question has four possible​ answers, one of which is correct. For students wh

o guess at all​ answers, find the variance for the number of correct answers. Round to the nearest tenth.
Mathematics
1 answer:
Aleks [24]3 years ago
5 0

Answer:

The variance for the number of correct answers is 2.8 questions

Step-by-step explanation:

The number of correct answers follows binomial distribution, in which we have:

  • n identical and independents events: the 15 questions
  • two possibles results that we call success and fail: The answer is correct and the answer is incorrect
  • probability p of success and 1-p of fail. Probability 1/4 of get the answer correct and probability of 3/4 of get the answer incorrect. This probabilities are calculated on that way because every question have 4 possible answers and one of which is correct.

So, the variance for a variable x that follows a Binomial distributions is:

V(x)=n*p*(1-p)

Then, the variance for the number of correct answers is:

V(x)=15*(1/4)*(3/4) = 2.8125 ≈ 2.8

Because n is equal to 15, p is equal to 1/4 and (1-p) is equal to 3/4.

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A quadratic function is a function of the form y=ax^2+bx+c where a, b, and c are constants. Given any 3 points in the plane, the
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Answer:

The quadratic function whose graph contains these points is y=-x^{2}-2x-2

Step-by-step explanation:

We know that a quadratic function is a function of the form y=ax^{2}+bx+c. The first step is use the 3 points given to write 3 equations to find the values of the constants <em>a</em>,<em>b</em>, and <em>c</em>.  

Substitute the points (0,-2), (-5,-17), and (3,-17) into the general form of a quadratic function.

-2=a*0^{2}+b*0+c\\c=-2

-17=a*-5^{2}+b*-5+c\\c=-25a+5b-17

-17=a*3^{2}+b*3+c\\ c=-9a-3b-17

We can solve these system of equations by substitution

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-9a-3b-17=25a+5b-17\\-9a-3b-17=-2

  • Isolate a for the first equation

-9a-3b-17=-25a+5b-17\\a=\frac{b}{2}

  • Substitute a=\frac{b}{2} into the second equation

-9\left(-\frac{b}{2}\right)-3b-17=-2

  • Find the value of b

-9\left(-\frac{4b}{17}\right)-3b-17=-2\\ b=-2

  • Find the value of a

a=\frac{b}{2}\\  a=-1

The solutions to the system of equations are:

b=-2,a=-1,c=-2

So the quadratic function whose graph contains these points is

y=-x^{2}-2x-2

As you can corroborate with the graph of this function.

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Answer:

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