A student takes a multiple-choice test that has 10 questions. Each question has four choices. The student guesses randomly at each answer. Let X be the number of questions the student gets correct. (a) Find P(X = 3). (b) Find P(X > 2). (c) To pass the test, the student must answer 7 or more questions correctly. Would it be unusual for the student to pass? Explain.

Answers

Answer 1

Answer:

1)0.2502

2)0.475

3)0.003505

Step-by-step explanation:

Total No. of question n= 10

There are four choices in each question

So, Probability of success [tex]p = \frac{1}{4}[/tex]

Probability of failure q  = [tex]1- \frac{1}{4}=\frac{3}{4}[/tex]

We will use binomial over here

[tex]P(X=x)=^nC_r p^r q^{n-r}[/tex]

1)

[tex]P(X = 3)=^{10}C_3 (\frac{1}{4})^3 (\frac{3}{4})^7\\P(X = 3)=\frac{10!}{3!7!} (\frac{1}{4})^3 (\frac{3}{4})^7\\P(X = 3)=0.2502[/tex]

2)  [tex]P(X > 2)=1-P(X\leq 2)[/tex]

P(X>2)=1-(P(X=0)+P(X=1)+P(X=2))

[tex]P(X>2)=1-(^{10}C_0 (\frac{1}{4})^0 (\frac{3}{4})^{10}+(^{10}C_1 (\frac{1}{4})^1 (\frac{3}{4})^9+^{10}C_2 (\frac{1}{4})^2 (\frac{3}{4})^8)[/tex]

[tex]P(X>2)=1-((\frac{1}{4})^0 (\frac{3}{4})^{10}+(\frac{10!}{1!9!} (\frac{1}{4})^1 (\frac{3}{4})^9+\frac{10!}{2!8!} (\frac{1}{4})^2 (\frac{3}{4})^8)[/tex]

P(X>2)=0.475

3)

[tex]P(X\geq 7)=P(X=7)+P(X=8)+P(X=9)+P(X=10)\\\\P(X\geq 7)=^{10}C_7 (\frac{1}{4})^7 (\frac{3}{4})^{3}+(^{10}C_8 (\frac{1}{4})^8 (\frac{3}{4})^2+^{10}C_9 (\frac{1}{4})^9 (\frac{3}{4})^1+^{10}C_{10} (\frac{1}{4})^{10} (\frac{3}{4})^0\\\\P(X\geq 7)=\frac{10!}{7!3!} (\frac{1}{4})^7 (\frac{3}{4})^{3}+\frac{10!}{8!2!} (\frac{1}{4})^8 (\frac{3}{4})^2+\frac{10!}{9!1!} (\frac{1}{4})^9 (\frac{3}{4})^1+\frac{10!}{10!0!}(\frac{1}{4})^{10} (\frac{3}{4})^0\\\\P(X\geq 7)=0.003505[/tex]


Related Questions

Jill runs 3/4 of a mile, and
Amy runs 2/3 of a mile.
How far did Jill and Amy
run combined?

Answers

Answer:

1 1/5 mile

Step-by-step explanation:

3/4 + 2/3 = 9/12 + 8/12 = 17/12 = 1 1/5

How do you do this question?

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Answer:

Divergent

Step-by-step explanation:

an = 3 sin(2/n)

Choose bn = 3 (2/n).

Using Limit Comparison Test:

lim(n→∞) an / bn

= lim(n→∞) [3 sin(2/n)] / [3 (2/n)]

= lim(n→∞) [sin(2/n)] / (2/n)

= 1

The limit is greater than 0, and bn diverges, so an also diverges.

What is the relationship between x and 86?

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Answer:

C

Step-by-step explanation:

the answer is C because they are on alternate sides and they are on the exterior meaning the outside.

Answer:

alternate exterior angles

Step-by-step explanation:

-cz+6z= tz+83
solve for z

Answers

Answer:

z =  83  /( -c+6-t)

Step-by-step explanation:

-cz+6z= tz+83

Subtract tz from each side

-cz+6z -tz= tz-tz+83

-cz+6z- tz=83

Factor out a z

z( -c+6-t) = 83

Divide by ( -c+6-t)

z( -c+6-t)/( -c+6-t) = 83  /( -c+6-t)

z =  83  /( -c+6-t)

Which is a perfect square?

Answers

Answer:

2 by 2

Step-by-step explanation:

or 4 by 4 I think I mean that would be mine

Answer:

The perfect squares are the squares of the whole numbers: 1 4 9 16 25 36 49, 64, 81, 100  Here are the square roots of all the perfect squares from 1 to 100. 1

Step-by-step explanation:

10a^2b^0 for a=–3, b=–8

Answers

Answer:

90

Step-by-step explanation:

Substitute a = -3 and b = -8 to the expression 10a²b⁰:

10(-3)²(-8)⁰ = 10(9)(1) = 90

a⁰ = 1 for any real number

Answer:

90

Step-by-step explanation:

10a^2b^0

Let a=–3, b=–8

10 (-3)^2 ( -8)^0

10 * 9 *1

90

evaluate the function when x = 5
P(x) = -3 + 4x

Answers

Answer:

P(x) = 17

Step-by-step explanation:

P(5) = -3 + 4(5)     <- Substitute X

P(5) = -3 + 20       <- Multiply

P(5) = 17                <- Combine Like Terms

Answer:

P(5)=-3+4(5)

P(5)=-3+20

P(5)=17

Evaluate the expression when b= 2.
12 - b =

Answers

Answer: 10

12-b

Substitute 2 in for b

12-2

Subtract

10

Answer:

Well, if b = 2, then 12 - b = 10

Step-by-step explanation:

hope this helps, lol! <3

Choose the fraction that goes in the blank 1/2< <4/5

Answers

Answer:

What are the answer choices?

Step-by-step explanation:

the circumference of the circle is 23 inches what is the radius of the circle?

Answers

Answer:

The radius is 3.66 if you need to round it would be 3.70.

Step-by-step explanation:

r= c/2[tex]\pi[/tex]

23/2pi= 3.66

The radius of the circle for the circumference of the circle is 23 inches is,

⇒ r = 3.66 inches

What is Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

The circumference of the circle is 23 inches.

Now, We know that;

The circumference of the circle = 2πr

Where, r is radius of the circle.

Hence, We get;

⇒ 2πr = 23

⇒ πr = 23/2

⇒ 3.14 × r = 11.5

⇒ r = 11.5 / 3.14

⇒ r = 3.66 inches

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An object is moving at a speed of 32 yards per hour. Express this speed in feet per day.

Answers

Answer

2304 feet per day

Step-by-step explanation:

The object will move 2304 feet per day.

What is speed ?

Speed is the distance an object moves in per unit of time.Speed is a scaler quantity because in speed the direction is not specified.

According to he given question an object is moving at a speed of 32 yards per hour.

We know 1 yard is = 3 feet.

∴ 32 yards is = 3×32 = 96 feet.

So, the object is moving at a speed of 96 feet per hour.

We also know that 24 hours is = 1 day.

The object moves 96 feet hour.

∴ The will move (96×24) feet per day.

= 2304 feet per day.

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As you can see, he uses one square for Stage 1, three squares for Stage 2 and six for Stage 3.


How many squares should he use for the sixth stage?​

Answers

Answer:

15 square for six stage

Answer:

21

Step-by-step explanation:

stage 1:  1

stage 2: 3

stage 3: 6

the pattern is that the number of squares increases everytime by the stage number it is. for example stage 2 has 3 squares. to find stage 3 you start off with 3 squares (from stage 2), and add the stage number (stage 3). 3+3=6 so stage 3 has 6 squares.

stage 4: 10 (6+4)

stage 5: 15 (10+5)

stage 6: 21 (15+6)

i cant find the answer to 2 1/4 times 1/6?.. can someone help a kid out

Answers

Answer:

0.375 or 3/8

Step-by-step explanation:

calculator :)

A falcon flew 70 miles in 3 hours. What was the speed of the falcon?

speed = distance over time

1 mile = 1609 meters.

Answers

Answer:

 37543.3333333 meters per hour

Step-by-step explanation:

The graph shows the relationship between the United States dollar and the euro, the currency of the European Union, in December 2011. Part A: What is the constant of proportionality shown in the graph? *

Answers

The graph is missing, so i have attached it;

Answer:

Constant of proportionality = 0.75

Step-by-step explanation:

From the graph attached, we are given 3 coordinate points of (x, y) namely;

(120, 90), (250, 187.5), (400, 300)

Now, constant of proportionality for each coordinate point is simply;

k = y/x

Thus, for first coordinate point (120, 90),

k1 = 90/120

k1 = 0.75

For 2nd coordinate point (250, 187.5),

k2 = 187.5/250

k2 = 0.75

For third coordinate point (400, 300),

k3 = 300/400

k3 = 0.75

From each of the 3 points, we can see the constant of proportionality is the same and equal to 0.75.

How does 5(x - 3) = 7x ÷ 2 become 10(x - 3) = 7x?

a.) Division Property
b.) Addition Property
c.) Multiplication Property
d.) Subtraction Property

Answers

Multiplication property

The grocery store sells cantaloupes for $4.50 per pound. Write a function c to
represent the cost for the number of pounds of cantaloupes bought, p.

Answers

Answer:

the equation is c=4.50p

Step-by-step explanation:

helpp meeee will award brainliest

Answers

What’s the question?

5. The total number of people who went to Disneyland this weekend was
6,405. If the ratio of boys to girls is 7 to 9 for those that attended, what was
the TOTAL number of boys and girls that went to Disneyland this weekend?
Show your work or explain your thinking.

Answers

Answer:

2,802 boys and 3,693 girls went to Disneyland this weekend

Step-by-step explanation:

System of Equations

Let's call:

b = Number of boys who went to Disneyland this weekend.

g = Number of girls who went to Disneyland this weekend.

The first condition states there was a total of 6,405 people who went to Disneyland this weekend, thus:

[tex]b+g=6,405\qquad\qquad [1][/tex]

The second condition states that the ratio of boys to girls is 7 to 9. This can be written as:

[tex]\displaystyle \frac{b}{g}=\frac{7}{9}\qquad\qquad [2][/tex]

To eliminate denominators, multiply [2] by 9g:

[tex]\displaystyle (9g)\frac{b}{g}=(9g)\frac{7}{9}[/tex]

Simplify:

[tex]9b=7g\qquad\qquad [3][/tex]

From [1]:

[tex]b=6,405-g[/tex]

Substituting into [3]

[tex]9(6,405-g)=7g[/tex]

Operating:

[tex]57,645-9g=7g[/tex]

Simplify:

[tex]16g=57,645[/tex]

Solve:

[tex]g=57,645 / 16 \approx 3,603[/tex]

Take the approximate value:

g=3,603

Find b:

[tex]b=6,405-3,603=2,802[/tex]

2,802 boys and 3,693 girls went to Disneyland this weekend

Note: Due to the nature of the problem, the results had to be rounded to the nearest integer. This condition makes the ratio not being exactly as required.

In other words it’s....?

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Answer:

ummmmmwm whatttt

Step-by-step explanation:

vbbbbhh

isisbeheuevevehebebdudibdebbeudiduehehdidieuwgeudidueheehwiqoapaopwpwpwpiwuwjueieiw. Hope this helps!!

Which quadratic equation gives the area A of the rectangle in square feet given its width in w feet

Given: (10,900) (20,1600)

Answers

Answer: 2nd choice on Ed

Step-by-step explanation:

Answer:

B

2400ft

Step-by-step explanation:

Approximately how many litres is 70 fluid ounces?

Use the conversion 20 fluid ounces = 1 pint and 1 3|4 pints = 1 litre

Answers

It’s about 2.7 could I have a brainliest plz and thank you and btw hope I helped

The value of 70 fluid ounces in liters would be, 2.065 liters

Used the concept of measurement unit that states that,

A measurement unit is a standard quality used to express a physical quantity. Also, it refers to the comparison between the unknown quantity with the known quantity.

To change 70 fluid ounces in liters.

Since we know that,

1 fluid ounce = 0.0295 liters

Hence, change the units of 70 fluid ounces in liters,

1 fluid ounce = 0.0295 liters

70 fluid ounce = 70 × 0.0295 liters

= 2.065 liters

So, we get;

70 fluid ounce = 2.065 liters

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4х + 1 cm
3х – 2 cm
Simplified

Answers

Answer:

x= -3

Step-by-step explanation:

4x+1=3x-2

4x-3x=-2-1

x={-3}

On a field trip, there are 3 adults for every 46 students. Which graph models a relationship with the same unit rate?

Answers

i’m pretty sure it’s H

Help ASAP
Find the difference
(2x + 6) - (7x + 3).

Answers

(2x + 6) - (7x+3)

= 2x + 6 - 7x - 3

=2x - 7x + 6 - 3

= -5x + 3

Answer:

The answer is (-5x + 3).

Step-by-step explanation:

Which ordered pairs are on the graph of 7x - y = 2?
(-3, -19)
(-1,-9)
(0, -2)
(1, 9)
(3,23)

Answers

Answer:

i think it is (0,-2). y=mx+b

(-1,-9) and (0, -2) lie on the graph of 7x - y = 2.

What is a graph in 2 - dimension?

A graph in two dimension is the set of points which relates two variables according to a give equation in two variables.

Given,

7x - y = 2

Therefore, the points which satisfy this equation lie on the graph of the equation.

In case of (-1,-9)

7(-1) - (-9) = 2

-7 + 9 = 2

Which is true.

Similarly for (0,-2)

7(0) - (-2) = 2

0 + 2 = 2

Which is true.

Hence, (-1,-9) and (0, -2) lie on the graph of 7x - y = 2.

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How to estimate the sum of using different methods. 187,176,154,207

Answers

Answer:

tuff

guess you will fail

Step-by-step explanation:

Fill in the blanks. a. A​ relative-frequency distribution is to a variable as a​ __________ distribution is to a random variable. b. A​ relative-frequency histogram is to a variable as a​ __________ histogram is to a random variable.

Answers

Answer:

a. A​ relative-frequency distribution is to a variable as a​ ___probability_______ distribution is to a random variable. b. A​ relative-frequency histogram is to a variable as a​ _____probability_____ histogram is to a random variable.

Step-by-step explanation:

Probability is a type of mathematics which deals with numerical descriptions of how likely an event would occur, or how likely it is that a the occurrence would be true. The probability of an event is usually between 0 and 1,

where 0 represent impossibility and 1 represents the chance of it occurring.

a. A​ relative-frequency distribution is to a variable as a​ frequency distribution is to a random variable.

b. A​ relative-frequency histogram is to a variable as a​  frequency histogram is to a random variable.

The relative frequency of an event is defined as the number of times that the event occurs during experimental trials, divided  by the total number of trials conducted.

A frequency distribution is an overview of all distinct values in some variable and the number of times they occur.

If there are many data points and we would like to see the distribution of the data, we can represent the data by a frequency histogram or a relative frequency histogram.

So, a. A​ relative-frequency distribution is to a variable as a​ frequency distribution is to a random variable.

b. A​ relative-frequency histogram is to a variable as a​  frequency histogram is to a random variable.

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In the game of​ roulette, a wheel consists of 38​ slots, numbered​ 0, 00,​ 1, 2,​ ..., 36. To play the​ game, a metal ball is spun around the wheel and allowed to fall into one of the numbered slots. The slots numbered 0 and 00 are​ green, the odd numbers are​ red, and the even numbers are black. To simulate outcomes from spinning the​ wheel, a researcher used the integer distribution to randomly generate 1000 numbers from 1 to​ 38, where 37 represents 0 and 38 represents 00.

Required:
a. What is the probability that the metal ball lands on green or red?
b. What is the probability that the metal ball does not land one green?

Answers

Answer:

hkkkkkkkkv

Step-by-step explanation:

khvvvvvvvvvvvvvvv

a cylinder made of metal has radius of 18 cm and height 40 cm if melted how many smaller cylinders of radius 2 cm and height 5 cm can be made

Answers

Answer:

648

Step-by-step explanation:

Volume of a cylinder =Pi× r²×h

volume of the cylinder before melted

v=Pi×18²×40

v=40715.04cm³

Volume of the smaller cylinder

v=Pi×2²×5

v=62.83

40715.04÷62.83

=648.019

=648 small cylinder can be made

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