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Svetradugi [14.3K]
3 years ago
12

A project is graded on a scale of 1 to 5. If the random variable, X, is the project grade, what is the mean of the probability d

istribution below?
                     Probability Distribution

.45    |
.4      |                            ~
.35    |                            ~
.3      |                            ~
.25    |                            ~
.2      |                ~          ~          ~
.15     |                ~          ~          ~
.1       |    ~          ~          ~          ~          ~
.05    |    ~          ~          ~          ~          ~
0       |__~____~_____~_____~____~____
              1          2          3          4          5
                                 X
Answer Choices:  A. 0.2  B. 0.4   C. 1  D. 3
Mathematics
2 answers:
choli [55]3 years ago
8 0

The correct answer is D) 3.

The mean is 3

damaskus [11]3 years ago
5 0

Answer:

3

Step-by-step explanation:

Given that A project is graded on a scale of 1 to 5.

If the random variable, X, is the project grade, we have to find  the mean of the probability distribution below

Since X takes values as 1,2,3,4,5

from the picture given we find the frequency distribution of X

X    1    2     3     4    5     Total

f     2    4     8     4    2       20

fx    2    8    24   16  10      60

Mean =60/20 =3

Hence answer is 3

   

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Given:

$\frac{12 x^{2}+31 x+7}{16 x^{2}+8 x+1}

To find:

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Solution:

Let us factor the numerator:

12 x^{2}+31 x+7

31x can be written as 3x + 28x.

    =\left(12 x^{2}+3 x\right)+(28 x+7)

Take 3x common in 1st two terms and 7 common in next two terms.

    =3 x(4 x+1)+7(4 x+1)

Make sure the remaining terms in the both brackets must be same.

Now, take out common factor (4x + 1).

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In the same way, factorize the denominator:

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8x can be written as 4x + 4x.

     =(16 x^{2}+4 x)+(4x+1)

Take 4x common in 1st two terms and 1 common in next two terms.

     =4x(4 x+1)+1(4x+1)

Make sure the remaining terms in the both brackets must be same.

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     =(4x+1)(4x+1)

Substitute the terms we found for numerator and denominator:

$\frac{12 x^{2}+31 x+7}{16 x^{2}+8 x+1}=\frac{(4 x+1)(3 x+7)}{(4 x+1)(4 x+1)}

Cancel the common factors.

                        $=\frac{3 x+7}{4 x+1}

The simplified expression is \frac{3 x+7}{4 x+1}.

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