2. Suppose that you are looking for a student at your college who lives within five miles of you. You know that 55% of the 25,000 students do live within five miles of you. You randomly contact students from the college until one says he or she lives within five miles of you.

(a) What is the probability that you need to contact four people?

(b) How many students from the college you expect to contact until you find one lives within five miles of you?

(C) What is the standard deviation of the number of students to be contacted until one says who lives within five miles of you?

(d) Suppose you randomly ask 5 students at your college, what is the probability that 3 of them live within five miles of you?

(e) Suppose you randomly ask 5 students at your college, what is the expected number of students who live within five miles of you?

How to do this five questions ? thanks​

Answers

Answer 1

Using the binomial distribution, it is found that:

a) There is a 0.0501 = 5.01% probability that you need to contact four people.

b) You expect to contact 1.82 students until you find one who lives within five miles of you.

c) The standard deviation is of 1.22 students.

d) There is a 0.3369 = 33.69% probability that 3 of them live within five miles of you.

e) It is expected that 2.75 students live within five miles of you.

For each student, there are only two possible outcomes. Either they live within 5 miles of you, or they do not. The probability of a student living within 5 miles of you is independent of any other student, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

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

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.

In this problem:

55% of the students live within five miles of you, thus [tex]p = 0.55[/tex].

Item a:

This probability is P(X = 0) when n = 3(none of the first three living within five miles of you) multiplied by 0.55(the fourth does live within five miles), hence:

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

[tex]P(X = 0) = C_{3,0}.(0.55)^{0}.(0.45)^{3} = 0.091125[/tex]

[tex]p = 0.091125(0.55) = 0.0501[/tex]

0.0501 = 5.01% probability that you need to contact four people.

Item b:

The expected number of trials in the binomial distribution until q successes is given by:

[tex]E = \frac{q}{p}[/tex]

In this problem, [tex]p = 0.55[/tex], and 1 trial, thus [tex]q = 1[/tex], hence:

[tex]E = \frac{1}{0.55} = 1.82[/tex]

You expect to contact 1.82 students until you find one who lives within five miles of you.

Item c:

The standard deviation of the number of trials until q successes are found is given by:

[tex]S = \frac{\sqrt{q(1 - p)}}{p}[/tex]

Hence, since [tex]q = 1, p = 0.55[/tex]:

[tex]S = \frac{\sqrt{0.45}}{0.55} = 1.22[/tex]

The standard deviation is of 1.22 students.

Item d:

This probability is [tex]P(X = 3)[/tex] when [tex]n = 5[/tex], hence:

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

[tex]P(X = 3) = C_{5,3}.(0.55)^{3}.(0.45)^{2} = 0.3369[/tex]

There is a 0.3369 = 33.69% probability that 3 of them live within five miles of you.

Item e:

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

Hence, since [tex]n = 5, p = 0.55[/tex]:

[tex]E(X) = 5(0.55) = 2,75[/tex]

It is expected that 2.75 students live within five miles of you.

A similar problem is given at https://brainly.com/question/25343741


Related Questions

if AB=12 cm and BC =13 cm then AC = 25 cm

Answers

Answer:

AB=12

Hope this helps!

a store pays $26 for a lamp. The store marks up the price by 40%. What is the amount of the markup

Answers

Answer:

$10.4

Step-by-step explanation:

mark me brainliest if u are kind

Which of the functions below have period pie check all that apply

Answers

There is no photo attached.

Answers:
A. 113 cm^3
B. 141 cm^3
C. 565 cm^3
D. 126 cm^3

Answers

Answer:

b

Step-by-step explanation:

SLOVE I GIVE BRAINLEST
18+ -27

A. -45

B. -9

C. 9

D. 48

Answers

Answer:

B: -9

Step-by-step explanation:

When you add a negative number, you subtract that number.

[tex]18+-27=18-27=-9[/tex]

18 + -27
= 18-27
= - 9
Answer will be B

Name the property of addition illustrated.

[3+(-8)] + 9 = 3+(- 8+9)

Answers

Answer:

Associative property

Step-by-step explanation:

The associative property states that, in addition, pairs of parentheses can be moved without changing the value of the expression. This means that (a+b)+c=a+(b+c). That same rule can be seen in the equation above because the parentheses move from the first 2 terms to the 3rd and 4th terms. Either way, both sides of the equation remain equal.

Here are two line segments with lengths e and f. Calculate the exact values of e and f. Which is larger? Use the Pythagorean Theorem: a^2 + b^2 = c^2

Answers

Just plug in the values, isolate the variables, then take the square root of the value

Write an equation of a line with an x-coefficient of - 3 and a y-intercept of 7

Answers

Answer:

y = -3x + 7

Step-by-step explanation:

For an equation in the format y = ax + b, a is the coefficient of x, and b is the y intercept.

Find the missing number in the following series: __ 85 81 83 79 81 77

Answers

Answer:

83

Step-by-step explanation:

The pattern is -4 then +2

Both questions 7 and 8

Answers

9514 1404 393

Answer:

  7.  $10,459.28

  8.  $30,060.93

Step-by-step explanation:

Your table 12-2 will tell you the present-value multiplier of the annual payment for a 10-year annuity due will be ...

  7%: 7.515232

  11%: 6.537048

__

7. The 11% table value will be used with a payment of $1600 to find the present value:

  6.537048 × $1600 = $10,459.28 . . . present value of the annuity due

__

8. The 7% table value will be used with a payment of $4000 to find the present value:

  7.515232 × $4000 = $30,060.93 . . . present value of the annuity due

10
Find the area of the shape.
Either enter on exact answer in terms of it or use 3.14 for it and enter your answer as a decimal.
units
Show Calculator

Answers

Answer:

(4-x)(x-4)=16-x2 help me please

Four times the product of a number x and a number y is equal to 20.

Answers

Step-by-step explanation:

4x×y=20

.....

..................................

The expression for four times the product of a number x and a number y is equal to 20 is 4xy = 20.

Given,

Four times the product of a number x and a number y is equal to 20.

We need to write the expression.

What is the meaning of the mathematical terms?

- 2 times M = 2 x M

- Product of M and N = M x N

- 3 more than M = M + 3

- 3 less than M = M - 3

Find the expression.

We have,

Four times the product of a number x and a number y is equal to 20.

Here,

The product of a number x and a number y can be written as:

= (x) x y

Four times the product of a number x and a number y can be written as:

= 4 x [ (x) x y ]

- is equal to 20 can be written as:

= 20

Now,

We get,

4xy = 20

Thus the expression for Four times the product of a number x and a number y is equal to 20 is 4xy = 20.

Learn more about how to write an expression here:

https://brainly.com/question/15284271

#SPJ2

pls help i think its 3600 but i dont know NO EXPLANATION JUST ANSWER

Answers

Answer:

16

Step-by-step explanation:

Set up a proportion

[tex]\frac{3}{45} = \frac{x}{240}[/tex]

Then, cross multiply.

[tex]720 = 45x\\16 = x\\x = 16[/tex]

I need help with number 5 please

Answers

Answer:

-4[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

I hope this helps!

Terrence has 100 points out of 200 possible points in his Geometry class.
A. Determine his grade as a percentage and letter grade. Explain how you determined this.
B. Calculate how many more points Terrence needs to be passing. Explain how you calculated this.​

Answers

Answer:

A. Letter Grade: F

    Percentage: 50%

    100 is half of 200

B. 20 more points

Step-by-step explanation:

A. 100 is half of 200, and 50% is half of 100%.

B. 60% is a D, but it is still passing. Sine 200=100 x 2, we need to multiply    60 x 2. 60 x 2=120

Pete worked 44 hours and 30 minutes on his new job. He makes $9.86 per hour. For each hour of overtime, he earns time and a half. How much will he earn for one week?

Answers

The question did not associate anything with the overtime so, I believe the answer is 416.24

:)

Answer:

$460.955 ≈ $460.96  

Step-by-step explanation:

A work week is 8 hours × 5 days = 40 hours per week.   Pete worked 44 hours and 30 minutes which is 44.5 hours.  This tells you that Pete worked 40 hours at regular paid and 4.5 hours of overtime at a rate is his amount per hour plus half of his amount per hour). So Pete earns $14.79 per hour for overtime rate  ($9.86 + $4.93 = $14.79) .

Earning for the week:  40 × $9.86 + 4.5 × $14.79

                                  = $394.40 + $66.555

                                  =  $460.955 ≈ $460.96  

                                 

A man is 32 years older than his son ten year ago he was three times as old as his son was then find the present age of each?

Answers

x-32=y

x-10=3(y-10)=3y-30

X+20=3y

3x-96=3y

Thus, X+20=3x-96, and 2x=116, X=58

Now, 58–32=y, thus, y=26

Would appreciate the help

Answers

i dont know :))))))))))))))))))))))

Uhm is this a function?

Answers

Yea because every input has only one output

Answer:

yes it is

Step-by-step explanation:

What is the answer to :
2x (4+3) -5 x [4-(9-7)]
??

Answers

Answer:

8×+6×-5×{2}

8×+6×-10×

14×-10×

calculation: 2x(4+3)-5x[4-(9-7)]

2x × 7-5x [4-(9-7)]

14x - 5x [4-(9-7)]

14x - 5x [2]

14x -5x × 2

14x - 10x

4x

As a bonus question on a test, Mr. Smith wrote 8z + (5y6w). He told his students the values of each variable: w=6, y=2, and z = 7. What is the simplification of Mr. Smith's expression?​

Answers

Answer:

416

Step-by-step explanation:

Plug in the variables

8(7) + (5*2 * 6*6)

56 + (10 * 36)

56 + 360

416


STRUCTURE Tell whether the triangles are similar.

Answers

Answer:

If two triangles have two pairs of sides in the same ratio and the included angles are also equal, then the triangles are similar.

Have a nice day and I hope this helps!

the area of a square is 36 centimeters. how long is each side of the square?

Answers

Answer:

6cm

Step-by-step explanation:

square root of 36 because the area of a square is base x height and a square has equal sides

Jon wants to earn at least $75,000 a year and live in a posh urban setting. James’s career plan includes earnings of $35,000 a year and simple, cheap living conditions. Whose lifestyle expectations are better?

Both are equally valid, they just have different preferences.

James’s, because he has more realistic expectations.

Jon’s, because he will have a higher quality of life

It depends on their career goals and family plans.

Answers

Answer:

Jon’s, because he will have a higher quality of life

Step-by-step explanation:

James wants to live in a cheap living condition so his quility is going to be worse. John wants to live in a posh urban setting and posh urban is higher quility than cheap living condition. So the anwser is C.

Answer:

Step-by-step explanation:

James

What is the first step needed to solve 3 over 4 multiplied by x minus 3 equals negative 18 ? (1 point) a Add 3 to both sides b Subtract 18 from both sides c Multiply both sides by 3 d Divide both sides by 4

Answers

Answer:

a

Step-by-step explanation:

3/4 x - 3 = -18

You should try to get all of one term on one side of the equation, and have the constant on the other side so the next step would be easy.

Here are the steps after you add 3:

3/4 x = -15

x = -5/4 (divide by 3/4 on both sides)

Answer is in the screenshot:

(5 1/4−2 1/2)+(6 2/3−3 1/2) plsss help (real answers)

Answers

Answer:

5 11/12. hope this helps

Step-by-step explanation:

Answer:

6

Step-by-step explanation: 5 1/4 - 2/12 = 3    6 2/3 - 3 1/2=3  3+3=6

Five tickets numbered 1, 2, 3, 4, and 5 are placed in a box, and three are selected at random. Determine the probability of obtaining a 1 or a 2 or both.

Answers

Answer:

the probability is 1 and 2

Only answer this if you know the answer.

Find The nth Term of this number sequence
18, 16, 14, 12

Answers

Answer:

2

Step-by-step explanation:

18,16,14,12,10,8,6,4,2

Pls mark me Brainly
Annswer:
2

Round to 2 decimal places 0.966

Answers

Answer:

Step-by-step explanation:

round to 2 places 0.966: 1.00

50 points! don't answer if you don't know! Thank You
#1 Jeanne's bank account earns interest annually. The equation shows her starting balance of ​$200 and her balance at the end of five ​years, ​$267.65. At what rate r did Jeanne earn​ interest?
r= ​%
​(Type an integer or decimal rounded to the nearest tenth as​ needed.)



#2 The volume of a soap bubble is 62.3mm^3 Find the radius and diameter of the soap bubble. Use 3.14 for pie.
The radius of the bubble is about mm.
​(Round to the nearest tenth as​ needed.)

Answers

Answer:

1. 6%

2. what is the radius of 2

Step-by-step explanation:

Answer:

#1 = Rate = 0.025

#2 = m^2

Step-by-step explanation:

#1

1. starting balance = 200

balance at the end of 4 years = 220.82

2. 200.82 = 200(1+r)^4

220.82

________  = (1 + r)^4

  200

1 + r = (1.1041)^1/4

1 + r = 1.025 - 1

r = 0.025

Rate = 0.025

#2

62.3m⋅m^3=62.3m^4

3.14=62.3m^4

m⋅m=m^2

Hope this helps, have a nice day/night! :D

If it did help please mark as brainliest!

Other Questions
Please help! I really need to get the answer correct Multiply (-2-i)(4+I) right answer only plz and thank u As discovered by researchers, high-achievement needs can be developed in people by teaching them how to: Guys Help po ... Ap - Ancient Egyptian Find and name 2 organizational patterns that made a social change in the world why is Ten dollars and Ice not a kinetic energy ? PLS HELP WILL MARK BRANLIEST ! NO FAKE ANSWERS!!! consider the sequences 31,35,39,43 ,then which of the following is the first terms of the sequences greater than 312 Can someone help me with this please? Does anyone know these answers? please help!!solve for x On June 30, Nance Company receives a $5,000, 90-day, 4% note from a customer as payment on her account. How much interest will be due on the note's maturity date Find 3(1.25). You may find using a number line to be helpful. 3(1.25) = under what condition could the weight of an object equal zero I need help with this asap 20. A sentence that consists of a single independent cause and makes a single statement is called a_____sentenceA. complerOB.compoundCunonOD. Simple A public opinion poll was administered to 50 people before the election of President Barack Obama. Polls taken before election night showed 50 percent of the people polled believed Barack Obama would be elected president. After the election results, the same people were asked if they believed Barack Obama would be elected president, and this time, 75 percent of the people said yes. This may be an example of ________ bias. Barbara wants to buy muffins. Which is the best deal? O a. 9 muffins for $7.92 O b. 4 muffins for $3.60 O c. 6 muffins for $5.34 O d. 8 muffins for $7.60 N Explain how hydrogen fuel cells work, and why they provide a healthy, clean way to produce heat and electricity. (Site 1).