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8 days ago

HOW DO YOU SEE IT The diagram represents the number of students in a school with brown eyes,

Mathematics

1 answer:

Zina [12.3K]8 days ago

3 0

a. true; the total number of individuals with brown hair is either the same as or exceeds those with brown eyes. b. false; the count of brown-haired individuals plus 10 can surpass the number of individuals with brown eyes, but cannot match it. c. true; the quantity of brown-haired individuals must exceed those with both brown hair and brown eyes. d. false; the sum of brown-haired individuals plus 10 can only exceed, not equal, the totals for both categories. e. true; the number of individuals with brown hair must outnumber both brown-haired and brown-eyed individuals. f. true; the count of brown-haired individuals plus 10 can solely surpass both counts. Hope this assists:)

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A standardized test consists of 100 multiple-choice questions. Each question has five possible answers, only one of which is cor

Zina [12379]

Response:

a) S ~ N (0, 48)

b) P(S > 10) = 0.0745

Detailed explanation:

Given Information:-

- Total number of questions, n = 100

- Each question has 5 options

- The probability of correctly guessing each answer is independent.

- Points for a correct answer = +4

- Points for an incorrect answer = -1

Inquiries:-

a) Determine????(S).

b) Determine P(S>10). Represent your response as a mathematical formula, then utilize the code cell below to calculate its numerical value, providing both the calculation and its result.

Solution:-

- The probability (p) for answering a question correctly is:

p (correct answer) = 1/5 = 0.2

- The expected number of correct and incorrect answers can be calculated as follows:

(Expected correct answers) = n*p = 100*0.2 = 20

(Expected incorrect answers) = n*(1-p) = 100*0.8 = 80

- The anticipated score for correct answers will be:

Sc(u) = (Points for a correct answer)*(Expected correct answers)

Sc(u) = (+4)*(20)

Sc(u) = 80 points

The anticipated score for incorrect answers will be:

Si(u) = (Points for an incorrect answer)*(Expected incorrect answers)

Si(u) = (-1)*(80)

Si(u) = -80 points.

- The average score a student might achieve would be S(u):

S(u) = Sc(u) + Si(u)

S(u) = 80 - 80 = 0

- The variance for both correct and incorrect answers can be calculated as:

Var(correct answers) = n*p*q = 100*0.2*0.8 = 16

Var(incorrect answers) = n*p*q = 100*0.2*0.8 = 16

- The variance of points for correct answers can be expressed as:

Sc(Var) = Var(correct answer) * (Points for a correct answer)

Sc(Var) = 16*(+4) = +64 points

- The variance of points for incorrect answers can be expressed as:

Si(Var) = Var(incorrect answer) * (Points for an incorrect answer)

Si(Var) = 16*(-1) = -16 points

- Since the probabilities of correct guesses are independent, according to the independence principle:

S(Var) = Sc(Var) + Si(Var)

= 64 - 16

= +48 points

- The standard deviation for the score distribution (s.d) is:

S(s.d) = √S(Var) = √48 = 6.9282

- Therefore, the anticipated score (S) from guessing on the MCQ test would yield a mean of u = 0 points and s.d = + 48 points.

- The random variable (S) can be approximated using normal distribution as follows:

S ~ N (0, 48)

- To find the required probability P(S>10).

Calculate the Z-value for S = 10 points:

Z-value = ( S - u ) / s.d

= ( 10 - 0 ) / 6.9282

= 1.4434

Consult the standardized Z-table for normal distribution:

P(Z > 1.4434) = 0.0745

The probability is:

P(S > 10) = P(Z > 1.4434) = 0.0745

5 0

1 month ago

The basketball team scored 82 points from 2- points anf 3-points baskets. They make 38 baskets altogether. Let a represent the n

Zina [12379]

Answer:

The linear equations are:

$2a+3b = 82$

$a+b=38$

Step-by-step breakdown:

Here, a denotes the quantity of 2-point shots, and b indicates the number of 3-point shots.

According to the information given:

The basketball team accumulated 82 points through 2-point and 3-point baskets.

⇒ $2a+3b = 82$

It is also stated that: They made a total of 38 baskets.

⇒ $a+b=38$

therefore, the linear equations are:

$2a+3b = 82$

$a+b=38$

7 0

1 month ago

Read 2 more answers

Calculating conditional probabilities - random permutations. About The letters (a, b, c, d, e, f, g) are put in a random order.

AnnZ [12381]

A="b is situated in the center"

B="c lies to the right of b"

C="The letters def occur sequentially in that arrangement"

a) b can occupy 7 positions; however, only one of these is the center. Therefore, P(A)=1/7

b) Let X=i; "b holds the i-th position"

Y=j; "c occupies the j-th position"

$P(B)=\displaystyle\sum_{i=1}^{6}(P(X=i)\displaystyle\sum_{j=i+1}^{7}P(Y=j))=\displaystyle\sum_{i=1}^{6}\frac{1}{7}(\displaystyle\sum_{j=i+1}^{7}\frac{1}{6})=\frac{1}{42}\displaystyle\sum_{i=1}^{6}(\displaystyle\sum_{j=i+1}^{7}1)=\frac{6+5+4+3+2+1}{42}=\frac{1}{2}$

P(B)=1/2

c) Let X=i; "d holds the i-th position"

Y=j; "e occupies the j-th position"

Let Z=k; "f is in the i-th position"

$P(C)=\displaystyle\sum_{i=1}^{5}( P(X=i)P(Y=i+1)P(Z=i+2))=\displaystyle\sum_{i=1}^{5}(\frac{1}{7}\times\frac{1}{6}\times\frac{1}{5})=\frac{1}{210}\displaystyle\sum_{i=1}^{5}(1)=\frac{1}{42}$

P(C)=1/42

P(A∩C)=2*(1/7*1/6*1/5*1/4)=1/420

$P(B\cap C)=\displaystyle\sum_{i=1}^{3} P(X=i)P(Y=i+1)P(Z=i+2)\displaystyle\sum_{j=i+3}^{6}P(V=j)P(W=j+1)=\displaystyle\sum_{i=1}^{3}\frac{1}{6}\frac{1}{7}\frac{1}{5}(\displaystyle\sum_{j=1+3}^{6}\frac{1}{4}\frac{1}{3})=1/420$

P(B∩A)=3*(1/7*1/6)=1/14

P(A|C)=P(A∩C)/P(C)=(1/420)/(1/42)=1/10

P(B|C)=P(B∩C)/P(C)=(1/420)/(1/42)=1/10

P(A|B)=P(B∩A)/P(B)=(1/14)/(1/2)=1/7

P(A∩B)=1/14

P(A)P(B)=(1/7)*(1/2)=1/14

Events A and B are independent

P(A∩C)=1/420

P(A)P(C)=(1/7)*(1/42)=1/294

Events A and C are not independent

P(B∩C)=1/420

P(B)P(C)=(1/2)*(1/42)=1/84

Events B and C are not independent

8 0

1 month ago

A box contains 4 red balls and 6 blue balls. A second box contains 16 red balls and unknown number of blue balls. a single ball

Leona [12618]

What options do you have?

4 0

12 days ago

Otto used 6 cups of whole wheat flour and x cups of white flour in the recipe. What is the equation that can be used to find the

tester [12383]

The recipe uses $x$ cups of white flower together with 6 cups of wheat flower.

Therefore, the combined quantity of flower equals $x+6$

If $y$ represents that combined amount, the equation to write is:
$y=x+6$

Constraints are as follows:
y can only be $\geq$ 6

Note that if y = 0 then x would have to be -6, which is not possible.

3 0

2 months ago

Read 2 more answers